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PRODUCTION AND MEASUREMENT 



OF 



HIGH VACUUM 



By 

SAUL DUSHMAN 

R esearch Laboratory, General Electric Company,, 
Schenectady, N. Y. 



PUBLISHED BY THE GENERAL ELECTRIC REVIEW 

SCHENECTADY, N. Y, 

1922 

X-5T5 



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Copyright 1922 
by General Electric Review 



XT***. 



NOV 16*23 



CIA 7 0027 9 



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PREFACE 



The present volume is an expansion and revision of a series 
of articles published in the General Electric Review during 1920- 
21. The subject of high vacua has become of such technical and 
scientific importance that it is hardly necessary to apologize for 
attempting to incorporate the information available on this topic 
into a convenient form for reference. 

Naturally the author has drawn to a large extent upon the 
results of numerous investigations carried out in this laboratory 
by Dr. Langmuir and his associates. To Dr. Langmuir, espe- 
cially, he wishes to express his sincere gratitude for constant 
encouragement and helpful suggestions. 

He also feels greatly indebted to Dr. Whitney for constant 
interest in the present undertaking, and for placing at his 
disposal the facilities of the laboratory for pursuing various 
lines of purely scientific work. 

An attempt has been made to give credit whenever possible 
to all those associated with the author in the field of high vacuum 
investigation and he can only say in addition that he has appre- 
ciated their constant co-operation and efforts in a line of work 
which is often accompanied by discouragements and negative 
results. 

The individual chapters were originally written as separate 
discussions, without any attempt at correlation. For the purpose 
of republication in book form, it was necessary to revise some 
sections completely and the reader may find errors both of 
omission and commission. The author will appreciate having 
his attention drawn to such cases. 



Research Laboratory, 

General Electric Company., 

Schenectady, N. Y. 
Sept. 1, 1922 



CONTENTS 

PAGE 

Introduction ". 1 

Chapter I. Kinetic Theory of Gases 

Laws of Boyle and Gay-Lussac.... 5 

Fundamental Postulates of the Kinetic Theory of 

Gases 5 

Velocity of Molecules . 6 

Maxwell's Law of Distribution of Velocities (Fig. 1) 8 

Molecular Velocities (Table I) . 9 

Relative Distribution of Molecular Velocities — Max- 
well's Law (Table II). 10 

Rate at which Molecules Strike a Surface . 1 1 

Application of Kinetic Theory to Determination of 

Vapor Pressures.. 12 

Mean Free Path of Molecules. 13 

Relation Between Coefficient of Viscosity and Mean 

Free Path ' 14 

Relation Between Coefficient of Velocity and Mean 

Free Path (Fig. 2) :7. :..! 14 

Coefficient of Viscosity and Average Free Path at 

Normal Pressure (Table III) 18 

Collision-Frequency , 19 

Direct Determination of Average Free Path..... 19 

References to Literature on Determination of Viscosity 

of Gases 19 

Relation Between Coefficient of Viscosity, Heat Con- 
ductivity and Diffusivity 21 

Coefficient of Heat Conductivity and Relation to 

Coefficient of Viscosity (Table IV) 22 

Relation Between Molecular Diameter and Mean Free 

Path 23 

Relation Between Molecular Diameter and Van der 

Waals' Constant b 25 

Molecular Diameters (Table V) 27 

General Considerations Regarding Gases at Low 

Pressure 28 

Laws of Molecular Flow 30 

Rate of Flow of Air and Hydrogen at Low Pressures 

and 20 deg. C. (Table VI) 32 

Laws of Flow at Higher Pressures 33 

Rate of Flow of Air at Different Pressures (Table VII) 34 

Thermal Molecular Flow 35 

Rate of Flow of Air at Different Pressures (Fig. 3) 35 

V 



PAGE 

Chapter II. High Vacuum Pumps 

Classification of Methods for the Production of Low 

Pressures 37 

General Theoretical Considerations Regarding 

Vacuum Pumps . 37 

Geryk Vacuum Pump, Power Drive (Fig. 4) 38 

Details of Construction of Geryk Vacuum Pump 

(Fig. 5) 41 

Gaede Piston Pump (Fig. 6) 42 

Mechanical Pumps 42 

Geryk Vacuum Pump 42 

Gaede's Piston Pump. 43 

Sprengel Pump 44 

Geissler-Toepler Pump 44 

Toepler Pump (Fig. 7) 45 

Gaede Rotary Mercury Pump (Fig. 8).... 46 

Speed of Exhaust with Toepler Pump (Table VIII) 47 

Gaede Rotary Mercury Pump..... 47 

Gaede Rotary Mercury Pump — Vertical Section 48 

Speed of Exhaust with Rotary Mercury Pump 

(Table IX) 49 

Gaede Rotary Mercury Pump — Diagrammatic View 

(Fig. 10)..... 49 

Rotary Oil Pump 49 

Improved Form Gaede Mercury Pump (Fig. 11) 50 

Gaede Molecular Pump 51 

Gaede Rotary Oil Pump, Side View (Fig. 12). 51 

Gaede Rotary Oil Pump, Front View (Fig. 13) • 52 

Standard Form of Rotary Oil Pump (Fig. 14) 53 

Diagram Explaining Operation of Molecular Pump 

(Fig. 15) 53 

Gaede Molecular Pump — Front View (Fig. 16) 54 

Gaede Molecular Pump — Side View (Fig. 17) 55 

Assembly of Gaede Molecular and Gaede Rotary Oil 

Pumps (Fig. 18) 56 

Effect of Speed of Rotation on Degree of Vacuum Ob- 
tained with Gaede Molecular Pump (Table X) 56 

Effect of Rough-pump Pressure on Speed of Gaede 

Molecular Pump (Fig. 19) 57 

Mercury Vapor Pumps 57 

Diagram Illustrating Principle of Diffusion Pump 

(Fig. 20) 58 

Gaede's Diffusion Pump 59 

VI 



PAGE 

Gaede Diffusion Pump (Fig. 21) 60 

Effect of Mercury Vapor Pressure on Speed of Diffu- 
sion Pump (Fig. 22) 61 

Effect of Pressure of Mercury Vapor on Speed of 

Exhaust with Diffusion Pump (Table XI) 62 

Effect of Width of Slit on Speed of Exhaust with Diffu- 
sion Pump (Table XII) 62 

Langmuir's Condensation Pump 63 

Langmuir Condensation Pump, Glass Form (Fig. 23) 64 

Condensation Pumps Built of Metal... 65 

Diagram of Construction of Condensation Pump, 

Metal Form (Fig. 24) 66 

Degree of Vacuum Obtainable 66 

Langmuir Condensation Pump, Metal Form (Fig. 25) 67 

Condensation Pump, Arc Type (Fig. 26) 68 

Other Forms of Mercury Vapor Pumps 68 

Crawford's Form of Condensation Pump, Vertical 

Type (Fig. 27). 69 

Crawford's Form of Condensation Pump, Horizontal 

Type (Fig. 28) 70 

General Remarks Regarding Exhaust Procedure 71 

Stimson's Form of Condensation Pump (Fig. 29) 72 

Vacuum Furnace for High Temperature Exhaust (Fig. 

30) 73 

Vapor Pressure of "Non-Condensible" Gases at Low 

Temperatures (Tables XIII) 76 

Arrangement of Exhaust System (Fig. 31) 77 

Vapor Pressure of "Condensible" Gases (Table XIV) 78 

Appendix I. 

Photograph of Set-up for Exhausting Coolidge X-ray 

Tubes (Fig. 32) 79 

Care of Condensation Pump 80 

Care of Rubber Tubing 80 

Mercury Trap 81 

Detection of Leaks 81 

Seal-Off Procedure 81 

Chapter III. Manometers for Low Gas Pressures 

Mercury Manometers 82 

Rayleigh's Gauge 82 

Rayleigh's Gauge (Fig. 33) 83 

VII 



PAGE 

Optical Lever Manometer (Fig. 34) 84 

McLeod Gauge (Fig. 35) 85 

McLeod Gauge . 86 

Mechanical Manometers 90 

Short Form of McLeod Gauge— Front View (Fig. 36) 90 

Short Form of McLeod Gauge— Rear View (Fig. 37) 91 

Viscosity Manometers 92 

Theory.... 92 

DecrementType of Viscosity Gauge 94 

Decrement Type of Gauge (Fig. 38) 95 

Quartz Fibre Gauge (Fig. 39) 96 

Optical Arrangement for Quartz Fibre Gauge (Fig. 40) 97 

Molecular Gauge (Fig. 41) 100 

Rotating Commutator Connection for Molecular 

Gauge (Fig. 42) 100 

Static Types of Viscosity Gauge.... 101 

Radiometer Gauges.... 102 

Crookes' Radiometer 102 

Knudsen Gauge.... 104 

Elementary Diagram of Knudsen Gauge (Fig. 43) 104 

Simple Construction of the Knudsen Gauge (Fig. 44) 106 
Woodrow's Modification of the Knudsen Gauge (Fig. 

45) 107 

Cross-sectional View Through the Middle of the Gauge 

Shown in Fig. 45 (Fig. 46) 108 

Electrical Connections of the Gauge Shown in Fig. 45 

(Fig. 47) 109 

Shrader and Sherwood's Modification of Knudsen 

Gauge 110 

Shrader and Sherwood's Modification of Knudsen 

Gauge (Fig. 48) Ill 

Resistance Manometers 113 

Hale's Improved Form of Pirani Gauge (Fig. 49) 1 13 

Pirani-Hale Gauge.. 114 

A Diagram of the Electrical Connections of the Gauge 

Shown in Fig. 49 (Fig. 50)...... 115 

Calibration Curves of the Gauge Shown in Fig. 49 

(Fig. 51) ... . 117 

Ionization Gauges 118 

Ionization Gauge and Connections (Fig. 52) 119 

Characteristic Curves of the Ionization Gauge (Fig. 

53) 121 



VIII 



PAGE 

Chapter IV. Sorption of Gases at Low Pressures 

Adsorption of Gases on Charcoal 123 

Dewar's Investigations on the Use of Charcoal in the 

Production of High Vacua 123 

Gas Adsorption on Charcoal (Table XV) l 124 

Absorption, Adsorption, Occlusion and Sorption 125 

Relative Adsorption of Hydrogen and Helium at Low 

Temperatures (Table XVI) . 125 

Adsorption of Gases on Charcoal, General Investiga- 
tions.. - . 126 

Adsorption of Gases on Charcoal at Low Pressures 

(Claude) (Fig. 54) 127 

Adsorption of Gases on Charcoal at Very Low Tem- 
peratures (Claude) (Fig. 55) 128 

Adsorption of Gases on Charcoal (Claude) (Table 

XVII) 129 

Adsorption of Gases on Charcoal (Titoff) (Table 

XVIII) 130 

Adsorption of Hydrogen and Nitrogen on Charcoal at 

Higher Temperatures (Claude) (Fig. 56) 131 

Comparative Adsorption of Different Gases (TitofI) 

(Table XIX) 132 

Adsorption of Argon on Charcoal (Homfray) (Fig. 57) 132 
Adsorption of Nitrogen on Charcoal (Homfray) (Fig. 

58) 133 

Adsorption of Carbon Monoxide on Charcoal (Hom- 
fray) (Fig. 59) 133 

Adsorption of Carbon Dioxide on Charcoal (Homfray) 

^ (Fig. 60) 133 

Sorption of Hydrogen by Charcoal at the Temperature 

of Liquid Air (Firth) (Table XX) „_. 134 

Use of Charcoal at Low Temperatures in High 

Vacuum Investigation. 134 

Adsorption on Charcoal at Low Temperatures (Extra- 
polated from Claude's data) (Table XXI) 134 

Rate of Clean-up by Charcoal 135 

Clean-up of Hydrogen by Activated Charcoal (M.Daly 

andS. Dushman) (Table XXII) 136 

Preparation of Charcoal, "Activated" Charcoal 137 

Absorption of Hydrogen by Palladium Black 142 

Absorption Relations 142 

Absorption of Hydrogen by Palladium Black (Valen- 

tiner) (Table XXIII) 143 

IX 



PAGE 

Preparation of Palladium Black 143 

Experiments on the Use of Palladium Black in the 

Productiortaf High Vacua 144 

Sorption of Gases by Glass, Metals and Other Sub- 
stances "-*.—. 146 

Sorption o"f Oases— General Remarks 146 

Adsorption of Gases on Different Adsorbents (Table 

XXIV) 147 

Sorption of Gases by Metals ..'. 148 

Weight of H 2 in mg. Dissolved by 100 g. Tantalum at 

760 mm. (Table XXV) 149 

Solubility of Hydrogen in Copper, Iron and Nickel 

(Fig. 61) . 150 

Dissociation Pressures in mm. Hg of Potassium and 

Sodium Hydrides (Table XXVI) 151 

Adsorption of Water Vapor 154 

Gases and Vapors Evolved from Glass and Metals at 

Very Low Pressures 156 

Evolution of Gas from Corning G-702-P Glass (Fig. 

62) . 158 

Evolution of Gas from Soda Glass (Fig. 63) 158 

Evolution of Gas from Ordinary Lead Glass (Fig. 64) 159 
Increase in Pressure in Sealed Bulb after Reheating 

(Fig. 65) . 161 

Amount of Dissolved Gases in Finished Glass (Table 

XXVII) 162 

Chapter V. Chemical and Electrochemical Clean-Up of 
Gases at Low Pressures 

Chemical Methods for the Clean-up of Residual Gases 165 

Clean-up of Gases by Calcium 165 

Clean-up of Residual Gases by Incandescent Tungsten 

Filaments 168 

Rate of Disappearance of Oxygen in Presence of Incan- 
descent Tungsten Filament at Different Tempera- 
tures (Fig. 66) 169 

Rate of Disappearance of Nitrogen in Presence of ' 

Incandescent Tungsten Filament (Fig. 67).... 171 

Electrical Clean-up of Gases at Higher Pressures 174 

Electrical Clean-up of Gases at Low Pressures 180 

Electron Emission Phenomena at Low Pressures 180 

Ionization Effects 181 

X 



. 









PAGE 

Illustrating Effect of Mercury Vapor on Characteristics 

of Hot Cathode Tube (Fig. 68) . 182 

Observations on Clean-up in Hot-cathodeJ^evices.. 183 

Hughes' Experiments on Clean-up of Gases *(Fig. 69) 188 

Clean-up and Glow Phenomena 189 

Relation between Pressure and Glow Potential for 

Various Gases (Campbell) (Fig. 70).... 189 

Electrical Clean-up Phenomena in Incandescent 1 Lamps 194 
Clean-up of Residual Air in 100-watt, 120-volt "Un- 

gettered" Lamp (Fig. 72) 196 

Clean-up of Residual Air in 100-watt, 120-volt 

"Gettered" Lamp (Fig. 73)... 197 

Clean-up of Argon and Air in 100-watt, 120-volt Phos- 
phorus "Gettered" Lamp, Flashed at 144 volts 

(Fig. 74) 198 

Rate of Clean-up in Two-filament Kenotron (Fig. 75) 199 
Theory Regarding Action of Phosphorus in Improv- 
ing Vacuum 200 

Chapter VI. Theory af Adsorption at Low Pressures 

Theory of Unimolecular Layer 204 

Adsorption at Low Pressures. 208 

Rate of Clean-up of Oxygen (Table XXVIII) 215 

Evidence for Adsorption Theory from Study of Effect 
H of Gases and Thorium on Electron Emission of 

Tungsten.... 217 

Evidence for Adsorption Theory Based on Viscosity 

Phenomena at Low Pressures 218 

"Temperature Drop" at a Surface in Gases at Low 

Pressures 221 

Recent Experiments of Wood and Knudsen on Con- 
densation. 223 

Concentration Drop at a Surface 227 

Significance of e and its Relation to the Accommoda- 
tion Coefficient 228 

Appendix II. 

Formulas from Kinetic Theory of Gases (Table I) 234 
Rate of Flow of Air and Hydrogen at Low Pressures 

and 20 deg. C 235 

Laws of Electron Currents in High Vacua (Table II) 236 

Molecular Data (Table III) 237 

Atomic and Electronic Constants (Table IV) 238 

XI 



FIGURES 

NO. PAGE 

1 Maxwell's Law of Distribution of Velocities 8 

2 Relation Between Coefficient of Viscosity and Mean 

Free Path . 14 

3 Rate of Flow of Air at Different Pressures 35 

4 Geryk Vacuum Pump, Power Drive 38 

5 Details of Construction of Geryk Vacuum Pump 41 

6 Gaede Piston Pump 42 

7 Toepler Pump ..: 45 

8 Gaede Rotary Mercury Pump 46 

9 Gaede Rotary Mercury Pump — Vertical Section 48 

10 Gaede Rotary Mercury Pump — Diagrammatic View 49 

11 Improved Form Gaede Mercury Pump 50 

12 Gaede Rotary Oil Pump — Side View 51 

13 Gaede Rotary Oil Pump— Front View.... 52 

14 Standard Form of Rotary Oil Pump .._.'. 53 

15 Diagram Explaining Operation of Molecular Pump 53 

16 Gaede Molecular Pump — Front View 54 

17 Gaede Molecular Pump — Side View.. 55 

18 Assembly of Gaede Molecular and Gaede Rotary Oil 

Pumps 56 

19 Effect of Rough-pump Pressure on Speed of Gaede 

Molecular Pump 57 

20 Diagram Illustrating Principle of Diffusion Pump 58 

21 Gaede Diffusion Pump. 60 

22 Effect of Mercury Vapor Pressure on Speed of Diffu- 

sion Pumps 61 

23 Langmuir Condensation Pump, Glass Form 64 

24 Diagram of Construction of Condensation Pump, 

Metal Form. 66 

25 Langmuir Condensation Pump, Metal Form... 67 

26 Condensation Pump, Arc Type. 68 

27 Crawford's Form of Condensation Pump, Vertical 

Type. 69 

28 Crawford's Form of Condensation Pump, Horizontal 

Type... 70 

29 Stimson's Form of Condensation Pump..... 72 

30 Vacuum Furnace for High Temperature Exhaust 73 

31 Arrangement of Exhaust System 77 

32 Photograph of Set-up for Exhausting Coolidge X-rav 

Tubes 79 

33 Rayleigh's Gauge 83 

XII 



NO. PAGE 

34 Optical Lever Manometer 84 

35 McLeod Gauge 85 

36 Short Form of McLeod Gauge, Front View... 90 

37 Short Form of McLeod Gauge, Rear View 91 

38 Decrement Type of Gauge 95 

39 Quartz Fibre Gauge... 96 

40 Optical Arrangement for Quartz Fibre Gauge. 97 

41 Molecular Gauge 100 

42 Rotating Commutator Connection for Molecular Gauge 1 00 

43 Elementary Diagram of Knudsen Gauge 104 

44 Simple Construction of the Knudsen Gauge 106 

45 Woodrow's Modification of the Knudsen Gauge 107 

46 Cross-sectional View Through the Middle of the 

Gauge Shown in Fig. 45 108 

47 Electrical Connections of the Gauge Shown in Fig. 45 109 

48 Shrader and Sherwood's Modification of the Knudsen 

Gauge.. Ill 

49 Hale's Improved Form of Pirani Gauge 113 

50 A Diagram of the Electrical Connections of the Gauge 

Shown in Fig. 49 115 

51 Calibration Curves of the Gauge Shown in Fig. 49... 117 

52 Ionization Gauge and Connections. 119 

53 Characteristic Curves of the Ionization Gauge 121 

54 Adsorption of Gases on Charcoal at Low Pressures 

(Claude) 127 

55 Adsorption of Gases on Charcoal at Very Low Tem- 

peratures (Claude).. 128 

56 Adsorption of Hydrogen and Nitrogen on Charcoal at 

Higher Temperatures (Claude) 131 

57 Adsorption of Argon on Charcoal (Homfray) 132 

58 . Adsorption of Nitrogen on Charcoal (Homfray) 133 

59 Adsorption of Carbon Monoxide on Charcoal (Hom- 

fray).... 133 

60 Adsorption of Carbon Dioxide on Charcoal (Homfray) 133 

61 Solubility of Hydrogen in Copper, Iron and Nickel 150 

62 Evolution of Gas from Corning G-702-P Glass 158 

63 Evolution of Gas from Soda Glass 158 

64 Evolution of Gas from Ordinary Lead Glass 159 

65 Increase in Pressure in Sealed Bulb after Re-heating 161 

66 Rate of Disappearance of Oxygen in Presence of Incan- 

descent Tungsten Filament at Different Tem- 
peratures. 169 

XIII 



NO. PAGE. 

67 Rate of Disappearance of Nitrogen in Presence of 

Incandescent Tungsten Filament... 171 

68 Illustrating Effect of Mercury Vapor on Character- 

istics of Hot Cathode Tube 182 

69 Hugh's Experiments on Clean-up of Gases __ 188: 

70 Relation between Pressure and Glow Potential for 

Various Gases (Campbell) 189' 

71 Typical Series of Observations at a Pressure of 0.156 

mm. of CO 193: 

72 Clean-up of Residual Air in 100-watt, 120-volt 

"Ungettered" Lamp 196 

73 Clean-up of Residual Air in 100-watt, 120-volt 

"Gettered" Lamp. 197 

74 Clean-up of Argon and Air in 100-watt, 120-volt 

Phosphorus Gettered Lamp, Flashed at 144 volts 19& 

75 Rate of Clean-up in Two-filament Kenotron 199 

TABLES 

I Molecular Velocities . 9 

II Relative Distribution of Molecular Velocities (Max- 

well's Law) 10' 

III Coefficient of Viscosity and Average Free Path at 

Normal Pressure 18 

IV Coefficient of Heat Conductivity and Relation to 

Coefficient of Viscosity 22 

V Molecular Diameters..... 27 

VI Rate of Flow of Air and Hydrogen at Low Pressures 

and 20 deg. C 32 

VII Rate of Flow of Air at Different Pressures 34 

VIII Speed of Exhaust with Toepler Pump 47 

IX Speed of Exhaust with Rotary Mercury Pump 49 

X Effect of Speed of Rotation on Degree of Vacuum 

Obtained with Gaede Molecular Pump 56 

XI Effect of Pressure of Mercury Vapor on Speed of 

Exhaust with Diffusion Pump 62 

XII Effect of Width of Slit on Speed of Exhaust with 

Diffusion Pump... 62 

XIII Vapor Pressure of "Non-Condensible" Gases, at 

Low Temperatures. 76 

XIV Vapor Pressure of "Condensible" Gases 78 

XV Gas Adsorption on Charcoal 124 

XVI Relative Adsorption of Hydrogen and Helium at 

Low Temperatures 125 

XIV 



NO. PAGE 

XVII Adsorption of Gases on Charcoal (Claude) 129 

XVIII Adsorption of Gases on Charcoal (Tit off) 130 

XIX Comparative Adsorption of Different Gases 

(Titoff) . 132 

XX Sorption of Hydrogen by Charcoal at the Tempera- 

ture of Liquid Air (Firth) 134 

XXI Adsorption on Charcoal at Low Temperatures 

(Extrapolated from Claude's data) 134 

XXII Clean-Up of Hydrogen by Activated Charcoal 

(M. Daly and S. Dushman) 136 

XXIII Absorption of Hydrogen by Palladium Black 

(Valentiner) 143 

XXIV Adsorption of Gases on Different Adsorbents . 147 

XXV Weight of H 2 in mg. Dissolved by 100 g. Tantalum 

at 760 mm 149 

XXVI Dissociation Pressures in mm. Hg of Potassium and 

Sodium Hydrides..... 151 

XXVII Amount of Dissolved Gases in Finished Glass 162 

XXVIII Rate of Clean-Up of Oxygen 215 



XV 



INTRODUCTION 

"Nature abhors a vacuum." This statement represents the 
•sum total of the knowledge possessed by the ancients of a field 
of scientific investigation which within the past decade has 
yielded results of extreme importance. In 1643, Torricelli, 
a pupil of Galileo, showed that nature abhors a vacuum to a 
limited extent and the discoverer of the fact that the atmos- 
phere exerts a pressure equivalent to that of a mercury column 
30 inches in height, is remembered by the designation "Torri- 
cellian vacuum" for the space above the mercury in the baro- 
metric tube. 

No doubt Torricelli imagined that this space is a "perfect 
void." We now know, however, that in this space there is 
mercury vapor at a pressure corresponding to about two or 
three million ths of an atmosphere and also traces of water vapor 
and air whose pressure may often amount to one or more 
millionths of an atmosphere. 

In 1654 Otto von Guericke invented the first mechanical 
air-pump which was subsequently improved by Boyle, Hawks- 
bee, Smeaton and others. During the two- hundred years or so 
that followed, the interest in low pressure phenomena was more 
or less academic and often that of the dilettante. The paths 
of glory laid out by Newton, Laplace and Maxwell in mathe- 
matical physics, and by Priestly, Lavoisier and Faraday in 
experimental science, were so enticing that little or no 
enthusiasm could be aroused in investigations of "empty 
space." However, with the development of the carbon filament 
lamp on the one hand, and the discovery by Geissler and 
others of curious electrical phenomena in gases at low pres- 
sures, there began a series of investigations in this field which 
have not only increased enormously our knowledge of the tech- 
nique for the production of lower and lower pressures, but have 
also led to results which have profoundly affected our views of 
the nature of matter and energy. 

When Crookes first observed the phenomena of cathode rays, 
he thought that he had discovered a fourth, or radiant state of 
matter. A further investigation of this subject by J. J. Thomson 
led him, as is well known, to the conclusion that in the con- 

1 



duction of electricity through gases at low pressures, the nega- 
tive current, or so-called cathode rays, is carried by extremely 
small corpuscles or electrons, whose mass is about one two- 
thousandths of that of a hydrogen atom while the charge is 
exactly the same as that carried by a hydrogen ion in elec- 
trolysis, but opposite, of course, in sign. These electrons are 
the principal carriers of the current in all cases of conduction in 
gases at low pressures. It was also observed that electrons are 
emitted from metals under the influence of light, and Richardson 
showed that electrons are emitted from incandescent metals. 
The conclusion was therefore drawn that electrons are present in 
the atoms of all elements — a conclusion which was very soon 
corroborated by observations on the radio-active elements. 

With the discovery by Roentgen of X-rays, the study of so- 
called vacuum tube phenomena entered upon a new phase 
which has led not only to increased knowledge of the structure 
of matter and the nature of X-rays, but also to vast improve- 
ments in both the devices for the production of these rays and 
their application to medical diagnosis and therapy. 

The mutual effects of purely scientific discovery and technical 
achievement have at no other time been better illustrated than 
in the history of the development of the hot cathode high 
vacuum devices which play such an important role at the 
present time in both the application of X-rays and of wireless 
telephony. The history of this development has been so inter- 
woven with the progress achieved during the past decade in the 
field of high vacua that a few remarks on this subject may not be 
out of place in this connection. 

It has already been mentioned that electrons are emitted from 
the surface of incandescent metals. A careful study of the 
variation in the number of electrons emitted per unit area with 
change in temperature led Richardson to the theory that the 
electrons are emitted from the metal by a process quite similar 
to that of ordinary evaporation. The mathematical relations 
are the same in both cases and, as in the case of ordinary molec- 
ular evaporation, it is also possible to calculate the heat of 
evaporation of the electrons for different kinds of surfaces. 

This view of the existence of an electron emission per ipse was 
opposed by a large number of investigators who maintained that 
the observed emission of electrons is a secondary effect due to 
chemical reactions at the surface, between the metal and the 
residual amount of gas present in the vessel. There was some 
excuse for this view, as Richardson's experiments were not car- 
ried out at very low pressures. The conclusion was therefore 






quite prevalent that in a "perfect vacuum" the electron emis- 
sion would disappear. 

A similar view was held with regard to the photo-electric 
effect, in which case electrons are emitted by the action of ultra- 
violet and ordinary visible radiation. 

In orderto throw some light on these problems, Dr. Langmuir 
carried out a series of experiments on electron emission in which 
special care was taken to obtain extremely low pressures. The 
results of this investigation showed that not only does the elec- 
tron emission persist even in the best obtainable vacuum, but 
that the rate of emission at any given temperature is a specific 
property of the metal. It was found that the power of emitting 
electrons is also greatly decreased by slight traces of different 
gases, even at very low pressures. However, if the vacuum is 
sufficiently good this electron emission is quite reproducible 
and constant, so that further improvement in degree of vacuum 
causes no increase in emission. It was also observed that at 
these low pressures the electron current exhibits space charge 
effects, that is, the mutual repulsion between the electrons 
emitted from the hot surface limits the further emission of elec- 
trons, and the electron current to the anode is then dependent 
upon the anode voltage. Such an effect could arise only under 
such conditions that the number of positive ions formed by 
collisions between electrons and gas molecules is extremely small, 
in other words, at very low gas pressures. This accounts for the 
fact that this phenomenon was not observed by previous inves- 
tigators. 

These discoveries immediately paved the way for develop- 
ment of the hot cathode X-ray tube by Dr. Coolidge and also 
led to the development of other hot cathode devices, such as the 
kenotron, pliotron and dynatron, whose application in wireless 
telephony and telegraphy has been of immense importance. At 
the same time the necessity for producing and maintaining high 
vacua in these devices has led to a vast amount of improvement 
in methods of exhaust. 

While the phenomena of electrical conduction in gases at very 
low pressures have thus served to arouse a great deal of interest 
in the subject of high vacua, a number of investigations in other 
fields of physics and chemistry have also led to greater interest 
in the same field. The work of Knudsen, Smoluchowsky, Gaede 
and others on the application of the kinetic theory of gases to 
low pressures, and the striking results obtained by Langmuir on 
the mechanism of chemical reactions at low pressures have led 
to new views upon the nature of chemical and physical forces 



between atoms and we can look forward, as a result of these 
investigations, to solving some of the most vexing problems in 
both physics and chemistry by a study of the phenomena in 
gases at very low pressures. 

Of necessity, as the technique of high vacuum production has 
improved, methods have been developed for measuring these 
extremely low gas pressures. A great deal of literature has been 
published during recent years on this whole subject, and a great 
deal of information has been gradually acquired in different 
laboratories about the actual technique of producing and measur- 
ing these pressures. In view of the important results to be 
expected from further investigations of low pressure phenomena 
it has been thought worth while to describe in the following 
chapters not only the methods available at present for the pro- 
duction and measurement of high vacua, but also to a lesser 
extent the more important results which have been obtained 
by the different investigators who have studied the physical 
and chemical phenomena exhibited in gases at very low pressures . 



CHAPTER I 
KINETIC THEORY OF GASES 

Laws of Boyle and Gay-Lussac 

The state of a gas is ordinarily defined by means of the 
volume which is occupied by a given mass under definite con- 
ditions of temperature and pressure. The three laws of Boyle, 
Gay-Lussac and Avogadro may be combined in the form of 
the well-known relation: 

PV=vRT (la) 

where P and V denote the pressure and volume respectively, 
T denotes the absolute temperature (degrees Centigrade + 273.1), 
v is the number of mols (mass in grams divided by the molec- 
ular weight) and R is a constant for all gases. 

The value of this constant is derived from the experimentally 
determined value of the volume of one mol of an ideal gas at 
given values of P and T. As standard pressure we shall consider 
that of 1 megabar. By definition, this is equal to 10 6 dynes per 
cm. 2 , and corresponds very closely to a pressure of 750 mm. 
of mercurv at deg. C, lat. 45 deg., and sea level. 

For t = 273.1 and P=l megabar, V = 22,708 cm. 3 per mol. 

Hence, R = 83. 15 X 10 6 ergs per degree abs. Denoting the 
weight of gas by co, and its molecular weight by M, equation 
(la) may therefore be written in the form, 

P F = 83.15X10 6 ^ (lb) 

where P is measured in bars (dynes per cm. 2 ) and V in cm. 3 

Now the pressures which we ordinarily deal w T ith in high 
vacuum phenomena range from 1 to 10~ 3 bar and even less. It 
is evident that at these pressures the volume of even a very 
small amount of any gas may be quite considerable. Thus, 
by applying the above equation to the case of hydrogen (M = 
2.016), we find that the volume occupied by 1 milligram of this 
gas at a pressure of 1 bar and 20 deg. C. (room temperature), 
is 1.209 X10 7 cm. 3 , while at standard pressure the volume is 
only 12.09 cm. 3 

Fundamental Postulates of the Kinetic Theory of Gases l 

For a proper understanding of phenomena in gases, more 
especially at low pressures, it is essential to consider these 

1 The reader will find more complete discussion of the kinetic theory of gases in the 
following books and articles: 

J. H. Jeans, The Dynamical Theory of Gases (1916). 
K. Jellinek, Lehrbuch der physikal. Chem. I. 1 (1914). 
W. C. McC. Lewis, Kinetic Theory of Gases (1915). 
O E. Meyer. Kinetic Theory of Gases. 

S. Dushman, The Kinetic Theory of Gases, General Electric Review, 15, 952. 1042, 
1159 (1915). 



6 Kinetic Theory of Gases 

phenomena from the point of view of the kinetic theory of 
gases. At the present time we can, as a matter of fact, regard 
this theory as much more than a mere hypothesis. The 
evidence of the actual existence of atoms and molecules is so 
conclusive that very few would care to believe to the contrary. 
On the other hand, the theory has enabled us to interpret and 
prophesy so many facts about gases that one naturally uses 
this point of view in discussing any phenomena in gases. 

The kinetic theory of matter, and more especially that of 
gases, rests essentially upon two fundamental assumptions. The 
first of these postulates is that matter is made up of extremely 
small particles or molecules, and that the molecules of the same 
chemical substance are exactly alike as regards size, shape, 
mass, and so forth. The second postulate is that the molecules 
of a gas are in constant motion, and this motion is intimately 
related to the temperature. In fact, the temperature of a gas is 
a manifestation of the amount of molecular motion. In the 
case of solids, at least those that are crystalline, it has been 
shown by the investigations of Bragg and others that the atoms 
which constitute the molecules when the substance is in the 
gaseous state are arranged in definite space-arrangements, and 
in this case the effect of temperature increase consists in increas- 
ing the kinetic energy of vibration of the atoms about their 
mean positions of equilibrium. 

But in the case of gases the effect of increased temperature 
is evidenced by increased translational (kinetic) energy of the 
molecules, and in fact, a relatively simple calculation based on 
these assumptions enables us to calculate the velocities of the 
molecules at any temperature. 

Velocity of Molecules 

According to the kinetic theory a gas exerts pressure on 
the enclosing walls because of the impact of molecules on these 
walls. Since the gas suffers no loss of energy through exerting 
pressure on the solid wall of its enclosure, it follows that each 
molecule is thrown back from the wall with the same speed 
as that with which it impinges, but in the reverse direction, that 
is, the impacts are perfectly elastic. 

Suppose a molecule of mass, m, to approach the wall with 
velocity G. Since the molecule rebounds with the same speed, 
the change of momentum per impact is 2 mG. If no molecules 
strike unit area in unit time with an average velocity G, the total 
impulse exerted on the unit area per unit time is 2 m no G. 






Kinetic Theory of Gases 7 

But the pressure is denned as the rate at which momentum is 
imparted to a unit area of surface. 
Hence, 

2mnoG = P (2a) 

It now remains to calculate no. Let n denote the number 
of molecules per unit volume. It is evident that at any instant 
we can consider the molecules as moving in six directions cor- 
responding to the six faces of a cube. Since the velocity of the 

n 
molecules is G, it follows that, on the average, - G molecules 



6 



will cross unit area in unit time. 

Equation (2a) therefore becomes 



p=L mn (;2 (2b) 

o 

From equation (2b) it is possible to deduce the three funda- 
mental laws of gases that have been mentioned. 

Since the product mn corresponds to the density, it follows 
that at constant temperature the pressure varies directly as the 
density, or inversely as the volume. This is known as Boyle's 
law. 

Again, from equation (2b) it will be seen that the kinetic 
energy of the molecules in a volume V is: 

-±-mnG 2 V = ^PV (3a) 

Now we know that if we mix two different gases that were 
previously at the same temperature there will be no change in 
temperature; this holds for all temperatures. Consequently, 
the average kinetic energy of the molecules (1 mG 2 ) must be 
the same for all gases at the same temperature and must increase 
at the same rate for all gases. We can therefore define temper- 
ature in terms of the kinetic energy of a gas. If we write 

\mnGW=%rRT (3b) 

where R is a constant, it immediately follows that 

PV = RT 
which is the law of Gay-Lussac. 

Lastly, let us consider equal volumes of any two different 
gases at the same pressure and temperature. Since P and V 
are the same for each, and i mG 2 is constant at constant tem- 
perature, it follows that n must be the same for both gases. 



8 Kinetic Theory of Gases 

That is, equal volumes of all gases at the same temperature and 
pressure contain an equal number of molecules. This was stated 
as a fundamental principle by Avogadro in 1811, but it took 
chemists about fifty years to understand its full import. 

If we let V denote the volume corresponding to the molec- 
ular weight, the value of the constant R is that defined by equa- 
tion (la). Instead of mn V we can write M, the molecular 
weight, and (3b) becomes 



±M(?~ 



RT 



(3c) 



Equation (3c) enables us to calculate the so-called mean 
velocity of the molecules. Substituting for R the value 83.15 
X 10 6 ergs per degree abs., we can write equation (3c) in the 
form: 



j^-lS.SOO^cm. 



sec. 



(3d) 



Table I gives the values of the mean velocity at deg. C, 
and 20 deg. C, for some of the more common gases. 

It follows directly from this equation that at constant tem- 
perature the rates of flow of different gases through a narrow 
opening must vary inversely as the square roots of the molec- 
ular weights. This conclusion is of importance in connection 
with exhaust problems since it indicates that heavier gases 
must be more difficult to pump out than lighter ones. 

Maxwell's Law of Distribution of Velocities 

It is evident that even if all the molecules in a given volume 
actually possessed the same velocity at any initial instant, the 






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N 


































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Fig. 1. Maxwell's Law of Distribution of Velocities 



Kinetic Theory of Gases 9 

collisions constantly occurring would disturb this equal distri- 
bution of velocities and a non-uniform distribution would soon 
be established. By applying the laws of probability, Maxwell 
showed that it is possible to calculate the law according to which 
the velocities of the molecules would be distributed at anv tem- 



TABLE I 
MOLECULAR VELOCITIES 







MEAN VELOCITY X 10 -5 CM. 






Gas 


M 


SEC 


• 1 


Average Velocity 
at 20° C. 
















At 0° C. 


At 20° C. 






H 2 


2.016 


1.838 


1.904 


1.755 X10 5 cm sec. 


-i 


o 2 


32.00 


0.4613 


0.4778 


0.440 




N 2 


28.02 


.4928 


.5106 


' .471 




Air 


28.96 


.4849 


.5023 


.463 




Hg 


200.6 


.1842 


.1908 


.176 




C0 2 


44.0 


.3933 


.4076 


.376 




H 2 


18.016 


.6148 


.6368 


.587 




A 


39.88 


.4133 


.4282 


.395 




NH 3 


17.02 


.6328 


.6554 


.604 




CO 


28.00 


.4933 


.5109 


.471 





perature. The curve shown in Fig. 1 represents graphically the 
distribution of velocities at any temperature, in terms of the 
most probable velocity, whose value is taken as unity. 

The equation of this curve is: 

4 2 -X 2 

y = —j=z% L e * 

V7T 

where y denotes the probability of a velocity whose magnitude 
is x times that of the most probable value. The significance of 
this curve can be understood better by means of the results 
tabulated in Table II. Under Ax is given the range of velocities 
and under Ay the fraction of the total number of molecules 
which have velocities corresponding to this range. Thus 16.1 
per cent of all the molecules have velocities which range be- 
tween 0.9 and 1.1 times the most probable velocity at any tem- 
perature. Similarly it follows that 68.4 per cent of the mole- 
cules have velocities ranging between 0.5 and 1.5 times the most 
probable velocity, while only 3.1 per cent have velocities that 
exceed 2.5 times the most probable velocity. 



10 Kinetic Theory of Gases 

TABLE II 

RELATIVE DISTRIBUTION OF MOLECULAR VELOCITIES 

(Maxwell's Law) 



Ax 


Ay 


Ax 


Ay 


-0.1 


0.001 


1.3-1.5 


0.112 


0.1-0.3 


.021 


1.5-1.7 


.078 


0.3-0.5 


.063 


1.7-1.9 


.058 


0.5-0.7 


.112 


1.9-2.1 


.034 


0.7-0.9 


.149 


2.1-2.5 


.030 


0.9-1.1 


.161 


2.5-3.0 


.008 


1.1-1.3 


.150 






0.5-1.5 


.684 


-2.5 


.969 



As shown in Fig. 1, the most probable velocity (which may be 
denoted by W) is different from the mean velocity, G, and the 
relation between these two values of the velocity is given by the 
following equation, which can be readily deduced from the equa- 
tion to the curve for Maxwell's distribution law: 



II 



& 



J 



2RT 
M 



= 12,900 



< 



M 



(4) 



In addition to these values of the velocity, it is important, in 
connection with a large class of applications of the kinetic theory 
of gases, to know the arithmetical or average velocity of the 
molecules at any temperature. This is usually denoted by ft 
and may be calculated by means of the relation, 



tt 



^8/3ir'G = J- 



8 RT 
Mir 



= 14,500 



4 



M 



(5) 



The values of the average velocity at room temperature for 
some of the more common gases are given in the last column of 
Table I. 

Number of Molecules Per Unit Volume 

According to Avogadro's law the number of molecules per 
gram-molecular weight of any gas ought to be the same. The 
problem of accurately determining the value of this constant, 
which we shall denote by N, has naturally been the object of a 
large number of investigations, and a number of different 



Kinetic Theory of Gases 11 

methods have been used in order to determine it. 2 The 
phenomena of Brownian movement, the accurate determination 
of the charge on an electron, counting the number of alpha par- 
ticles expelled from a gram of radium, and finally the study of 
the laws of black bod}'- radiation — all these methods have led 
to approximately the same value for N. According to Millikan, 
whose determination is undoubtedly the most accurate we have, 
this constant has the value of 6.062 X10 23 . From this value it 
is readily calculated that the number of molecules per cubic centi- 
meter of an ideal gas at a pressure of 10 6 bars and deg. C, is 
2.67 X10 19 . 

Let us now attempt to interpret this magnitude. The highest 
vacua attainable at present range around 10~ 4 bar. Even at 
this extremely low pressure, which would ordinarily be regarded 
as a "perfect vacuum," the number of molecules per cm. 3 , at 
deg. C, is still 2,670,000,000, a number which is, roughly 
speaking, of the same order of magnitude as the total population 
of the earth. 

From the above considerations it follows that at any tempera- 
ture T and pressure P, the number of molecules per cm. 3 is given 
by the relations : 

NP P 

n = -^^ = 7.29 X 10 15 ^ (press, in bars) (6) 

Kl 1 

P 
= 9.71X10 1 ™ (press, in mm. of mercury). 

This is the significance attached to n in the following chapters. 

Rate at Which Molecules Strike a Surface 

It was shown by Meyer that the number of molecules of a gas 
at rest as a whole that strike unit area per unit time is equal to 
\in 12. 

Substituting for n and 12 the values previously given, we obtain 
the relation. 

p 
1/4 n 12 = 2.653 X10 19 -t -(press, in bars) (7a) 

Vmt 

For air at 20 deg. C, and 10 6 bars, the number of molecules 
striking 1 cm. 2 per second, is 2.88 X10 23 . 

Equation (7a) may also be expressed in terms of the mass (w) 
of gas that strikes 1 cm. 2 per second. 

2 For a detailed. discussion of the different methods which have been used for the deter- 
mination of Avogadro's number, N, the reader is referred to the following: 
J. Perrin, Les Atomes. 
S. Dushman, General Electric Review, IS, 1159 (1915). 



12 Kinetic Theory oj Gases 

Let p denote the density of the gas, and m the mass per mole- 
cule. 

™ MP 

Then, P = -^j 

and w = 1/4 n m ft = 1/4 p Q = 43.74 X 10~ 6 PJ-=r gm. cm.- 2 sec.- 1 

V (7b) 

For air at 20 deg. C, and 10 6 bars, 
w = 13.8 gm./cm. 2 sec. 

Application of Kinetic Theory to Determination of Vapor Pressures 

An interesting application of equation (7) has been made by 
Langmuir to the calculation of vapor pressures from rates of 
evaporation of metals in high vacua. As this subject is discussed 
at further length in a subsequent chapter it will be sufficient in 
the present connection to quote from Langmuir's paper on 
"The Vapor Pressure of Metallic Tungsten." 3 

' ' Let us consider a surface of metal in equilibrium with its 
saturated vapor. According to the kinetic theory we look upon 
the equilibrium as a balance between the rate of evaporation and 
rate of condensation. That is, we conceive of these two processes 
going on simultaneously at equal rates. 

"At temperatures so low that the vapor pressure of a sub- 
stance does not exceed a millimeter, we may consider that the 
actual rate of evaporation of a substance is independent of the 
presence of vapor around it. That is, the rate of evaporation 
in a high vacuum is the same as the rate of evaporation in pres- 
ence of saturated vapor. Similarly we may consider that the 
rate of condensation is determined only by the pressure of the 
vapor. " 

It is therefore possible, according to Langmuir, to apply 
equation (7) to calculate the vapor pressure of a metal like 
tungsten from the observed rate of evaporation (loss of weight 
at constant temperature) in vacuum. 

Thus, at a temperature of 2800 deg. K., the observed value 
of o), the loss in weight of a tungsten filament is 0.43 X 10 -6 gms. 
per square cm. per second. Substituting in equation (7b) we 
find for P, the value 28.6 X 10" 6 mms. of mercury, or 38.1 X10~ s 
bar. 

In the same manner Langmuir and Mackay 4 have obtained 
the vapor pressure curves of the metals tungsten, molybdenum 
and platinum over a large range of temperatures. 

» Phys. Rev. 2, 329 (1913). 
<Phys. Rev. 4, 377 (1914). 




Kinetic Theory of Gases 18 

Mean Free Path of Molecules 

While the individual molecules in a gas at rest possess very 
high velocities, as previously shown, it is a matter of ordinary 
observation that gases diffuse into each other very slowly. This is 
explained on the kinetic point of view by assuming that the 
molecules do not travel continuously in straight lines, but 
undergo frequent collisions. The use of the term "collision" 
naturally leads to the notion of free path. This may be defined 
as the distance traversed by a molecule between successive 
collisions. Since, manifestly, the magnitude of this distance is 
a function of the velocities of the molecules, we are further led 
to use the expression "mean free path" (denoted by L), which is 
denned as the average distance traversed by all the molecules 
between successive collisions. 

However, this definition assumes that the molecules actually 
collide like billiard balls; that is, the molecules are assumed to 
be rigid elastic spheres possessing definite dimensions and exert- 
ing no attractive or repulsive forces on each other. This, 
however, can certainly not be in accord with the facts. We have 
every reason to believe that the structure of atoms and molecules 
is exceedingly complex. It is probably impossible to state 
definitely what is the diameter of a hydrogen atom or molecule. 
Also there is no doubt that the molecules exert attractive forces 
on each other for certain distances and repulsive forces when 
they approach exceptionally close. Otherwise how could we 
explain surface-tension, discrepancies from Boyle's law, and a 
host of related phenomena? To speak of collisions among 
molecules such as these is impossible. What meaning, there- 
fore, shall we assign to the free path under these conditions? 

It is readily seen that the most essential idea at the back of 
the term "free path" is this: We imagine it possible to take a 
cinematograph picture of the molecules in a given portion of 
space; we then consider their velocity components in a given 
direction and find that at the end of a certain distance L the 
average value of the velocity components of all these molecules 
taken in the same direction has decreased by a certain amount; 
in other words, the average number of molecules traveling in 
the given direction is less after they have traversed the 
distance L. On this basis, the term free path has a physical 
meaning which is independent of all ideas that we may form of 
the actual structure of the molecules or of the nature of the 
inter-molecular forces. 

Another method of overcoming the same difficulty is to 
investigate the relations between the free path and the other 



U 



Kinetic Theory of Gases 



properties of a gas, assuming rigid spherical molecules with or 
without attractive forces, and then consider the case of any 
actual gas in terms of this hypothetical gas. 

Evidently the mean free path must depend upon the molec- 
ular diameter, and simple considerations indicate that the 
length of the mean free path must vary inversely as the total 
cross-sectional area of the molecules per unit volume. Again, 
the magnitude of the coefficients of viscosity, heat conductivity 
and diflusivity of gases are intimately bound up with the length 
of the free path; whether it be transference of momentum from 
one layer to another as in viscosity, or transference of increased 
kinetic energy of the molecules as in heat conductivity, the rate 
of this transference must depend upon the number of collisions 
which each molecule experiences as it passes from point to point. 
We thus obtain relations between the mean free path, the 
coefficients of viscosity and heat conductivity on the one hand, 
and on the other hand, equations that connect the mean free 
path with the molecular diameter. 

Relation Between Coefficient of Viscosity and Mean Free Path 

A gas streaming through a narrow bore tube experiences 
a resistance to flow, so that the velocity of this flow decreases 
uniformly from the center outwards until it reaches zero at the 
walls. Each layer of gas parallel to the direction of flow exerts a 
tangential force on the adjacent layer tending to decrease the 







Fig. 2 



Kinetic Theory of Gases 15 

velocity of the faster-moving and to increase that of the slower- 
moving layers. The property of a gas (or liquid), in virtue of 
which it exhibits this phenomenon, is known as internal viscosity. 

As a simple working hypothesis we may assume, as Newton 
did, that the internal viscosity is directly proportional to the 
rate of decrease of velocity in the different gas layers. Further- 
more, the viscosity must depend upon the nature of the fluid, so 
that in a more viscous fluid the tangential force between adjacent 
layers, for constant rate of decrease of velocity, will be greater 
than in the case of a less viscous fluid. We thus arrive at the 
following definition of the coefficient of viscosity: 

The coefficient of viscosity is defined as the tangential force 
per unit area for unit rate of decrease of velocity. 

With this definition we are in a position to deduce the ap- 
proximate form of the relation between the coefficient of vis- 
cosity and the free path. 

Let u denote the velocity of flow of the gas at a distance 
d from a stationary surface. In the case of uniform flow along a 
surface, the velocity will decrease uniformly to zero as the sur- 
face is approached. We can therefore represent, as in Fig. 2, 
the velocity at distance OA=d by the ordinate AB = u and 
velocities at intermediate distances by the corresponding or- 
dinates below the line OB. 

We shall imagine the gas divided into layers parallel to 
the surface, each having a depth equal to the free path, L. 

Let us denote the tangential force per unit area between 
adjacent layers by B. By definition: 

B = rj X velocity-gradient 

= ^f (8) 

where r\ denotes the coefficient of internal viscosity. 

. But according to the kinetic theory, the tangential force 
per unit area is measured by the rate at which momentum is 
transferred per unit area between adjacent layers. 

Owing to the relative motion of the layers, the molecules 
moving from a faster into a slower moving layer possess more 
momentum in the direction of flow than those moving in the 
opposite direction. 

Let us consider any layer, CE or EH of thickness equal to 
L. We have chosen this particular value of the thickness so 
that we may be justified as a first approximation in assuming 
that the molecules starting at either of the planes CD or EF 
reach the opposite plane without suffering collision, that is, 
without change of momentum. 



16 Kinetic Theory of Gases 

The momentum, parallel to the surface, of any molecule 
reaching the plane EF from the plane CD is m{u' +G), where 
u' denotes the velocity of flow at the plane CD and G is the mean 
velocity of the molecules. 

The momentum, parallel to the surface, of a molecule reach- 
ing the plane EF from the plane HK is m(u' + G+2 t tk). 

The number of molecules that cross unit area per unit 

time in any direction in a gas at rest is equal to — nG, and this 

must be the same for the molecules traveling in a direction 
perpendicular to the plane EF, for the velocity of flow is as- 
sumed to be so small that the density remains constant through- 
out the different layers. 

Hence the net rate of transference of momentum across 
unit area of the plane EF is equal to 

B = \mnG^ (9) 

From equations (8) and (9) it follows that 

7] = —mnGL=—pGL (10) 

o • o 

In deducing this equation it has been assumed that the 
molecules all possess the same velocity G and the same free 
path L. It is evident therefore that the equation thus derived 
cannot be accurate. Introducing Maxwell's law of distribution 
of velocities, Boltzmann deduced the equation 

?7 = 0.3502 pQL (11) 

where ft = average velocity 

= 14551V 7 T/M cm. sec." 1 
and L is defined as the average free path. 

Meyer in his "Kinetic Theory of Gases" used a different 
method of calculation and derived a relation of the form, 

?7 = 0.3097 ptoL' (12) 

This is the relation usually adopted in text books on physics. 
On the other hand, the more recent publications, such as those of 
Jaeger, 5 Millikan and Fletcher, 6 and others, prefer Boltzmann's 
formula. Following the latter authorities we have made use 



5 Fort, der Kinetische Gastheorie. 

6 Phys^Rev. 4. 440 (1914). 



Kinetic Theory of Gases 17 

in the following calculations of equation (11) to determine the 
so-called mean or average free path.* 

From the preceding equations an interesting conclusion 
may be deduced regarding the dependence of viscosity on 
pressure. As has been mentioned, it is evident from very 
simple considerations that L varies inversely as the number of 
molecules present per unit volume. Consequently the product 
pL is constant and independent of the pressure. The velocity, 
ft, depends only upon the temperature and molecular weight. 
It therefore follows that, for any gas at constant temperature, 
the viscosity is independent of the pressure, and must increase 
with the temperature. The confirmation of these two deductions 
has been justly regarded as one of the most signal triumphs 
of the kinetic theory of gases. As is well known, the viscosity 
of all ordinary liquids decreases with increase in temperature. 
That the viscosity of gases must increase with temperature 
was therefore regarded as a remarkable conclusion. 

At both extremely low pressures and very high pressures, 
the conclusion that the viscosity is independent of the pressure 
is not in accord with the observations, but this is due to the 
fact that the same derivation as has been used above is not valid 
under those conditions where either attractive forces between 
the molecules come into play or the pressure is so low that a 
molecule can travel over the whole distance between the walls 
of the enclosure without suffering collision.! 

According to the preceding equations, it is therefore possible 
to calculate L for a gas under given conditions from data on 
the viscosity. In Table III are given the values of L=r]/ 
(0.3502 /oft) calculated for different gases at deg. C. and 20 
deg. C. and 10 6 bars. The values of p have been calculated 
from molecular weights, while the values of ft have been taken 
from Table I. 

In choosing values of r]o (the viscosity at deg. C.) from 
the large amount of data available in the literature, an attempt 
has been made to choose the most recent and most accurate 
values in each case. The authorities for the different data are 
given in the footnote to Table III. For rj 2 o (the viscosity at 20 

* In German text-books, L is referred to as "mittlere freie Weglange." The term 
"mean free path" is used by English writers, most of whom adopt Meyer's formula. In 
view of the fact that we may have several different "means," we prefer the unambiguous 
designation ''average free path." 

r , „_ . 0.3502 _ ._ ,. . 

U (Meyer) = 3QQ7 L (Boltzmann) 

= 1.131 L (B) 
t The observations on viscosity effects at low pressures are discussed in the latter part 
of this chapter and also in Chapter VI. 



18 



Kinetic Theory of Gases 



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o 


NN00O 




I>o6»OOcd^H'*^00'-<0 


X 


NOOt>CDOWrO--nCiOo 


<£= 


(M t-h!>cOCMC<ItM>05(M 




T— ( ' ' 7— 1 ,-1 T-l T-H l-< T^ 








, , 




? s 


O 




i— 1 


03CO^©0(M^ooc»(MO 


X 


OOOcOOiNiOcD'-hcoi>iM 


o 


oooocio>roi>t>o<N^co 


P? 


1—1 t— 1 H ,H H Ql (M H |Q 




v3v3 cuO^ P-sb-ii ^ * 


U 


LO 00 CO 




cDLCfMOOOQ'-'OCNas 




1>1>>0^0'-^COCD"<^ 




COlOHHHH(M 




'^S^S^^^S'^'F^ 


o 


~~ ■"• ' S -"-~-"- N 'v *"" ' 




X 


-COOO^OOiON»00 


gp 


h^NhO^DNOONN 




I>0000OiCT3CDCOCi'-^COCO 




,_ _ ^h^h^CSJ^h^h 


O 


•*s - *>^9,o « « 6 *« 




^EtjtCj^tCJo^iO^OfcC! 



Kinetic Theory of Gases 19 

deg. C.) the experimentally observed value has been used in the 
case of air, while in all other cases use has been made of 
Sutherland's equation.* 

( 27Z.l+C \ /293.1\f , 1Q , 

™=i\w*I+c) (ml) (13a) 

where C is a constant for each gas. 

Collision-Frequency 

From the values of L and 9 we obtain the collision-fre- 
quency, fi/L, that is, the average number of collisions per 
second. These are given in the last column of Table III for 
room temperature. Thus, a molecule of nitrogen under ordinary 
conditions suffers over 5000 million collisions per second. It 
is not surprising, therefore, that gases diffuse relatively slowly. 

Direct Determination of Average Free Path 

The magnitude of the average free path under normal 
conditions is extremely small. As seen from Table III it is 

about 10 -5 cm. or -—r mil. But as the pressure decreases the 

free path increases. At 1 bar, which is about the degree of 
vacuum attained in exhausting ordinary incandescent lamps, 
the average free path for most gases is between 5 and 10 cms. 
A molecule of tungsten evaporated from the filament suffers 
very few collisions, if any, in traveling to the walls of the bulb, 
as is evident from the sharp boundaries of the blackened por- 
tions. 



References to Literature on Determination of 77 

The literature on this subject is very extensive. Fortunately most 
of 'the data have been summarized by Fisher [Phvs. Rev. 24, 385 (1904); 
Chapman, Phil. Trans. A. 211, 433 (1911), and Gilchrist, Phys. Rev. 
1, 124 (1913)]. The latter's determination of the coefficient of viscosity 
for air is probably the most accurate value available of this constant, 
and has been used by Millikan in his precision measurement of the charge 
on an ion. According to Millikan [Ann. Phys. 41, 759 (1913)], the most 
accurate value for the coefficient of viscosity of air is 
v t =0.00018240 - 0.000000493 (23 - 1) 
(23>t>l2) 
According to this relation, 

77,0 = 0.0001809 
For 770, Prof. Millikan quotes three values, see (a), whose average 
0.0001711 we have used as probably the most accurate value. 

*The derivation of this equation is discussed on pages 24 and 25. 



20 Kinetic Theory of Gases 

So far as the writer is aware the only investigators who have 
made any direct determination of the free path are Lenard, 8 
Robinson, 9 and Franck and Hertz. 10 

The method used by all of these was the same — that of 
determining the average distance traversed by a gaseous ion 
between collisions. A charged molecule (ion) if endowed with 
a sufficiently high velocity, is capable of producing other ions 
by collision. It is therefore possible to measure the minimum 
distance at which two plates must be placed in a gas in order 
that it may be possible for the ions passing from one plate to 
the other to produce fresh ions by collision. Franck and Hertz 
obtained the following results: 





Pressure 

(Bars) 


L 
(Cm.) 


L CALC. (t = 20 DEG. C.) 


Gas 


(Meyer) 


(Boltzmann) 


H 2 
He 


45 
81 

152 
1670 

124 


0.436 
0.256 
0.146 
0.014 
0.256 


0.438 
0.243 
0.130 
0.012 
0.250 


0.388 
0.215 
0.115 
0.011 
0.221 



References to Literature on Determination of r\ {Cont'd) 

Vogel [Ann. 4-3, 1235 (1914)] has carried out similar measurements 
in the case of other gases. As he referred his results to 770 for air = 1724 
X10 7 , we have re-calculated them to correspond with the above value. 
These are referred to as Vogel's corrected values. 

The other authorities to whom reference has been made are: 

Kaye and Laby 's Tables of Constants (K. & L.). 

Jellinek's Physikal. Chem. I, 1, p. 305-7. 

Markowski, Ann. Phys. 14, 742. 

In the following references, C, F and V denote Chapman, Fisher 
and Vogel respectively. 

(a) Breitenbach, 1708.7; Fisher, 1709.2; Holman, 1715.7. 

(b) V, 844; C, 854; Markowski, 841. 

(c) F. (d) V, 1862; C. 1885. (e) F, 76.2; C, 75.3. 

(f) V. (g) V. (h) Jellinek. (k) V. (m) K. & L. The values 

in square brackets are for 100 deg. C. (n) V. 

(p) F. (q) V, 1666; C, 1672; Markowski, 1674. 

(r) F, 110.4; C, 111.7; V, 110.6. 

(s) V, 1905; C, 1900. 

(t) C, 1303; F, 131.1; V, 133. 

(u) C, 2107; V, 2100. (v) C. (w) V, 1370; F, 1387. 

(x) C, 249; V, 277; K. & L. 240. (y) K. & L. 

(z) K. & L. The values in square brackets are for 300 deg. C. 



8 Lenard, Ann. Phys. 12, 714 (1903). 

9 Robinson, Phys. Zeit. 11, 11 (1910). 

!» Franck u. Hertz, Deutsch. Phys. Ges. 14, 596 (1912); 15, 373 (1913). 



Kinetic Theory of Gases 21 

The observed values of L appear to agree better with the 
values calculated according to Meyer's equation (12). The 
experimental evidence is, however, insufficient to be able to 
form from it a definite conclusion as to which equation is really 
more satisfactory. 

It ought to be observed in this connection that for an 
infmitesimally small particle in a gas the mean free path accord- 
ing to Maxwell is 4V~2 L, where L is the free path for the gas 
molecules themselves. This relation has been applied to calculate 
the free path for electrons in gases. However, there is at present 
little or no experimental evidence in justification of this pro- 
cedure. In fact, in some recent experiments by Mr. C. G. 
Found and the writer with the ionization gauge, the results 
obtained led to the conclusion that the mean free paths are much 
greater than those expected from the above relation. Partzsch 11 
has also found that in the case of photo-electrons colliding with 
gas molecules the actually observed values of the mean free 
paths are about twice as great as those calculated from Maxwell's 
formula. 

Relation Between Coefficient of Viscosity, Heat Conductivity and 
Diffusivity 

The kinetic theory of gases achieved a great triumph when 
it led to the conclusion that the viscosity is independent of the 
pressure. It led to still further important results when it proph- 
esied the existence of simple relations between the coefficients 
of viscosity, heat conductivity and diffusivity. 

From the kinetic point of view it is the same whether the 
molecules transfer momentum from one layer to another or 
translational energy. The equations are quite analogous. 

As in the case of viscosity, we consider any two layers 
CE, EH (Fig. 2), each of thickness L, between two plates whose 
temperatures are 7\ and T 2 and distance apart d. Let c v denote 
the heat capacity per unit mass. The relative temperature 
drop between the planes CD and HK is equal to 

2 (T.-T^ 

Hence the heat transferred per unit area is 

Q= —n G. 2 m c v ; — — 

6 d 

= ^ pGc '- L — T~' 



" Ann. d. Phys. 44, ">56 (1914). 



Kinetic Theory of Gases 



Therefore the coefficient of heat conductivity, 
k= —p G c v L. 



(H) 



From equations (10) and (14) it follows that 

k= 7] c v (15a) 

A more accurate calculation of the heat conductivity shows 
that this equation is not quite correct, and should be written 

k = B rj c v (15b) 

where B is a constant (greater than unity) , whose value depends 
upon the nature of the forces that are assumed to exist between 
the molecules and upon the structure of the molecules themselves. 

Similarly it can be shown that the diffusion constant of 
one gas into any other is proportional to the coefficient of 
viscosity. The relations are, however, quite complicated. 

Chapman 12 has shown that the value of the constant B 
must be very closely equal to 2.5 for monatomic gases, 1.90 
for diatomic gases, and less than this for polyatomic gases. 
These conclusions have been confirmed experimentally by 
Eucken. 13 

Table IV taken from Eucken 's paper gives the values of 
k (experimentally determined by Eucken), rj (Vogel's data)* 
and cv together with the observed values of B at 7 = 273. 

TABLE IV 

COEFFICIENT OF HEAT CONDUCTIVITY AND RELATION 

TO COEFFICIENT OF VISCOSITY 



Gas 


feXlO' 


TjXIO? 


c v 


B Obs. 


B Calc. 


He 

A 


3360 
390 


1876 
2102 


0.746 
0.0745 


2.40 \ 
2.49 / 


2.50 


H 2 

N- 2 
Oi 
CO 
NO 


3970 
566 
570 
542.5 
555 


850 
1676 
1922 
1672 
1794 


2.38 

0.177 

0.155 

0.177 

0.1655 


1.965 n 
1.905 
1.913 
1.835 
1.870 J 




1.90 


CO; 

H 2 
NH 3 


337 

(429) 
513.5 


1380 

1006 

926 


0.1500 

0.342 

0.388 


1.628 

1.25 

1.43 





12 S. Chapman, the Kinetic Theory of a Gas Constituted of Spherically Symmetrical 
Molecules, Phil. Trans. A, 211, 433 (1911). 

"Eucken, Phys. Zeit. 14, 324 (1914). See also Jeans, Dynamical Theory of Gases, 
p. 317. 

* No correction has been applied to any of the data given in Table IV, as the intention 
was merely to illustrate the variations in the value of B. 



Kinetic Theory of Cases 23 

Relation Between Molecular Diameter and Mean Free Path 

As mentioned previously, recent speculations on the struc- 
ture of the atom lead to the conclusion that atoms and mole- 
cules are far from being the rigid elastic spheres postulated 
by the founders of the kinetic theory. According to the present 
theory of atomic structure we must conceive of the atom as 
consisting of a positively charged nucleus surrounded by one 
or more rings of electrons. The diameter of the nucleus is 
extremely small (less than 1/100,000) compared to the diameters 
of the electronic orbits, so that it is possible for the alpha 
particles, which have the same mass as helium atoms, to 
pass right through an atom of a heavy metal like gold. It is 
therefore certain that in the case of chemical combinations the 
atoms have inter-penetrated to form the molecule. The evi- 
dence deduced by T. W. Richards on the compressibility of 
atoms is also in accord with these views. On the other hand, it 
may be reasonable to speak of the diameter of a molecule if 
we think of it as the smallest distance apart to which the centers 
of two molecules can approach. Even this definition may not 
be accurate, but we can make use of it as a physical basis for 
mathematical relationships. 

Denoting the molecular diameter by d m , it was shown by 
Clausius 14 that in the case of spherical molecules all possessing 
the same velocity G, the length of the free path is 

L=- —, ps (16) 

4 TV n dm 2 

If we take into account the fact that the molecular velocities 

vary according to Maxwell's distribution law, it can be shown 

that the average free path 

L = - T J (17) 

V2irnd m 2 

Jeans has, however, pointed out that this equation cannot 
be accurate, since it takes no account of the persistence of veloci- 
ties after collision. 15 "On the average, a collision does not re- 
verse the velocity in the original direction of motion, or even 
reduce it to rest, but there is a tendency for the original velocity 
to persist after collision." Jeans shows that in the case of two 
similar molecules colliding with relative velocities that may 
vary all the way from to °° , the average value of the persistence 

2 
is very nearlv equal to - of the value when the molecules col- 



See Jellinek, pp. 287-292. 
Meyer's Kinetic Theory, pp. 161-3. 
Jeans, Dynamical Theory of Gases, p. 276, etc. 



2J+ Kinetic Theory of Gases 

lide with equal velocities. That is, on the average, the mole- 
cules traveling in a given direction will after collision have lost 

sixty per cent! - lof their velocity component in that direction. 



G) 



Hence, according to Jeans, the equation should be written 

1 319 * 

L= _ J (18) 

V 2 7T n d m 2 

According to Chapman, Jeans' formula is not quite correct. 
He has shown that for the case of rigid elastic spheres with no 
attractive forces, 

0.4909 _ , im 

9 =—7= p!2 (19) 

Comparing equation (19) with equation (11) it is seen that, 
according to Chapman, 

, 0.4909 



0.3502 V2tt« 

1.402 
V 2 7T n d m 2 



(20) 



This formula is true only for rigid elastic spheres with no 
attractive forces. Assuming the existence of such forces, the 
effect obviously must be to shorten the free path, and in ac- 
cordance with Sutherland's 16 conclusion we must write for 
equation (20) the relation 

L = L402 



V2 ir n dj 



H) 



where C is a constant for each gas whose value may be deter- 
mined from the temperature coefficient of the viscosity. 

*This manner of denning the free path could obviously be extended to the case of mole- 
cules obeying any other law of force, where no collisions (according to the literal meaning 
of the word) occur. It has already been observed in a previous paragraph (p. 13) that 
we might define L in terms of the ratio of the molecules traveling in a given direction at 
one point to the number traveling in the same direction at a point further along in the same 
direction. Jeans' concept of persistence of velocities leads us therefore to the following def- 
inition of average free path which would hold in all cases except that of unlike molecules. 
We can define the average free path as being twice the distance which the molecules traveling 
at any instant in a given direction will pass over before losing sixty per cent of their velocity 
component in that direction. The factor 2 is required because at any instant the mole- 
cules have, on the average, covered one-half the distance between collisions. 

This definition has been suggested to the writer by Dr. I. Langmuir and although 
it may not be the usual definition, the latter is so vague that a scientifically correct defini- 
tion would certainly help to clear the prevailing misunderstanding about the whole subject 
of free paths. 

16 Phil. Mag. 36, 507 (1893). 



Kinetic Theory of Gases 25 

This equation, combined with equations (19) and (11), 
leads to the following expression for the variation with tempera- 
ture of the coefficient of viscosity: 

*i-*»(?f£) (mj (13b) 

Sutherland's equation has been found to be in excellent 
agreement with the experimental data. The assumption there- 
fore appears to be justified that the molecules approximate 
fairly closely to rigid elastic spheres surrounded by attractive 
fields of force. 

Equation (21) combined with equation (11) and a knowl- 
edge of n enables us to calculate the molecular diameter from the 
coefficient of viscosity. 

Relation Between Molecular Diameter and Van der Waals' Constant, b 

At very high pressures or temperatures so low that the 
gases can condense, it is observed that Boyle-Gay-Lussac's 
equation 

PV = RT 
is no longer applicable. 

Van der Waals found that the behavior of gases near their 
critical temperature and pressure 17 could be expressed quanti- 
tatively by a modified form of the above equation as follows : 

( P +Vi) (v- b> ) = RT ( 22 ) 

In this equation, a/V 2 is a correction term added to P, 
which takes into account the attractive forces exerted by the 
molecules upon each other. The constant b denotes a small 
volume whose magnitude compared to the molecular volume, 
V, becomes of importance when we are dealing with gases near 

their critical state. According to Van der Waals, - is equal to 



the total volume c 
That is, 


if the molecules. 




TV- 7I " J -3 

4 6 


or 


d3 _ 3.6 



(23) 

Z 1\ TV 

where N = 6.062 X10 23 . 



17 S. Dushman, ' "The Absolute Zero, " General Electric Review, February and April, 1915. 



26 Kinetic Theory of Gases 

The value of the constant b may be determined for each 
gas from the critical temperature (T c ) and pressure (P c ) by means 
of the relation : 

b = RT c /8P c (24) 

In this equation b denotes the volume in cm 3 per molecular 
weight. Ordinarily this constant is given in tables in terms of 
the volume of the gas at 0°C. and 1 atmosphere pressure as 
unity. Denoting the latter by b t it is evident that b in the above 
equations corresponds to 6* X 22,412. 

Jeans has pointed out 18 that since b and a in Van der Waals' 
equation are not constant down to the critical temperature and 
pressure, values of b calculated by means of equation (24) are 
probably far from accurate. He therefore recommends cal- 
culating b from the observed deviations from Boyle's law as 
expressed by equation (22). 

There is still a third method by which the molecular diam- 
eter may be calculated. According to Clausius and Mossotti, 
the volume actually occupied by the molecules may be cal- 
culated from either the dielectric constant D or the refractive 
index i by means of the equations : 



6 



G 



(26) 



Table V gives the values of the molecular diameter cal- 
culated for different gases by each of these methods. The 
first column gives the values of d m calculated from the average 
free path, L, according to equation (21). 

The values of C and L have been taken from Table III. 

The second column gives the values calculated recently by 
S. Chapman 19 and A. O. Rankin e 20 by a slightly modified form 
of the same equation. 

Column III gives the values, calculated by Chapman by 
means of equation (23), using the values of b obtained from the 
observed deviation from Boyle's law. Column IV gives values 
calculated from the data on critical temperature and pressure by 
means of equation (24) . The critical data used were those given 
by Jellinek. 21 Column V gives the values of dm calculated by 

18 Dynamical Theory of Gases, p. 174, etc. 
» Phil. Trans. Roy. Soc. A. 216, 279 (1916). 
20 Proc. Roy. Soc. 98, 360 (1920). 
« Physikal Chem. I, 1, pp. 444-5. 



Kinetic Theory of Gases 



O. Sackur 22 from the refractive index for the D-line. These 
data have been corrected for the difference between the values of 
K used by Sackur and by the writer. Calculations on the 
magnitude of the molecular diameters are also given by J. L. 
Jeans, 23 R. Eucken 24 and A. Heydweiller. 25 

The general agreement between the results given in the 
first three columns is very satisfactory. In view of Jeans' 
criticism just mentioned, the values in Column IV cannot be 
considered as having nearly the same degree of accuracy as those 
in Column III, while the values in Column V indicate that this 
method gives only approximate results. 

As has been pointed out by Rankine 20 the above arguments 
are all based on the assumption that the molecules are spherical. 
"When we come," he writes, "to consider the case of diatomic 
molecules— as, for example, in chlorine gas— we are met with the 
difficulty that we are no longer entitled to regard the molecule 

TABLE V 

MOLECULAR DIAMETERS 

Unit 10~ 8 cm. 



Gas 


I 


II 


III 


IV 


v 


Hi 


2.403 


2.38 


2.52 


2.341 


1.91 


N t 


3.146 


3.13 


3.08 


3.146 


2.41 


0, 


2.975 


2.96 


2.89 


2.919 


2.32 


He 


1.905 


1.91 


1.96 


2.646 


1.18 


Ne 




2.35 








A 


2.876 


2.87 


2.85 


2.939 


2.36 


Kr 




3.19 


3.14 






Xe 




3.51 


3.42 






Ch 










3.33 


Br 2 










3.88 


1-2 










4.56 


Hg 








3.013 




H 2 








2.887 


2.28 


CO 


3.190 






3.121 


2.52 


COt 


3.335 


3.30 


3.40 


3.231 


2.78 


NH 3 


2.967 






3.080 





as a sphere. Hitherto, it has been necessary to regard it as 
such, and obtain, by the formula which is strictly applicable to 
single atoms only, an average atomic diameter. All viscosity 
formulae merely enable us to calculate an average value of wd w 2 
which is trie area presented as a target by the molecule to other 



2- Ann. Phys. 40, 87 (1913) 

23 Dynamical Theory of Gases, p. 341, 

*« Phys. Zeits. 14, 324 (1913). 

25 Ann. Phys. 42, 1273 (1913). 



28 Kinetic Theory of Gases 

molecules approaching it from all possible directions." Rankine 
has therefore attempted to calculate the actual arrangement of 
the atoms in a molecule such as 2 on the basis of the Lewis- 
Langmuir theory of atomic structure, utilizing the values derived 
by W. L. Bragg for the radii of the atoms in crystalline com- 
pounds. 26 The conclusion arrived at is that the best model for 
such diatomic molecules is an ellipsoid of revolution whose 
longer diameter lies along the line joining the centers of the two 
atoms. 

General Considerations Regarding Gases at Low Pressure 

As has already been stated, the pressures which interest us in 
the study of high vacuum phenomena usually range below 1 bar. 
At these pressures the mean free paths of the molecules are at 
least of the same order of magnitude as the dimensions of the 
vessels used in experimental work. Thus, at 1 bar the mean free 
paths for most gases are about 10 cm. (Table III). It therefore 
follows that the majority of the molecules travel in straight lines 
as far as the dimensions of the vessels will allow, and the num- 
ber of inter-molecular collisions per second becomes relatively 
small as compared with the rate at which the molecules strike 
the walls. The following considerations will probably serve to 
explain the significance of this statement more fully. 

Consider a cube, whose volume is D* cubic cm., and let n 
denote the number of molecules per cm. 3 . The number of colli- 
sions between gas molecules per second is 

The total number of molecules striking the walls of the cube 
in each second is 

A=6D 2 n% 



Hence, -p; oo — . 



That is, the ratio between the rate at which 



the molecules strike the walls and the rate at which they collide 
with each other is given by the ratio between the lengths of the 
mean free path and of the side of the cube. It can be readily 

shown that no matter what the shape of the vessel, the ratio -•= 

is proportional to that of -=r, where D is the distance between the 

walls. Thus, if D is of the order of magnitude of 10 cm., A is 
greater than C when L is greater than 10 cm., that is, when the 

« Phil. Mag. 40, 169 (1920). 



Kinetic Theory of Gases 29 

pressure is lower than 1 bar (approximately). Consequently we 
should expect to find that at pressures of 1 bar and lower, the 
molecules travel in straight lines toward the walls of the contain- 
ing vessel. 

A very common illustration of this fact is the production of 
sharp shadows in vacuum type incandescent lamps. As has been 
shown by the investigations of Langmuir and Mackay, 27 the 
blackening of ordinary tungsten lamps is due to the evaporation 
of metal from the filament. The pressure in this type of lamp 
under operating conditions is less than 0.01 bar, 28 so that the 
mean free path of the tungsten atoms is of the order of several 
hundred centimeters. Consequently, collisions between these 
atoms and molecules of residual gas are very rare, and the tung- 
sten atoms travel directly to the sides of the bulb, where they are 
immediately condensed. By interposing some object between 
the filament and the walls, very sharp shadows can be produced, 
if the vacuum is good. On the other hand, the shadows are very 
much blurred if there is present in the bulb a pressure of even 
several bars of some inert gas like argon. Similar phenomena are 
observed in the evaporation of other metals, like mercury and 
sodium. 29 

This observation that at very low pressures it is possible to 
obtain very well defined shadows by the evaporation of metals 
has been applied recently by O. Stern 30 to measure directly the 
translational velocity of molecules. The principle of the method 
used is as follows : 

The vapor produced by evaporation from a metallic filament 
in a very good vacuum is allowed to pass through a hole L, and a 
screen with a circular aperture is placed in front of the hole. 
The beam of molecules passing through the hole L and the 
opening in the screen forms a sharply defined circular spot on 
a plate P at a distance from the screen. If now the whole 
apparatus, including screen and plate P, is rotated about an axis 
perpendicular to the path of the molecules and passing through 
the hole L, the spot formed on P is displaced in a direction 
opposite to that of rotation by an amount 5 which may be cal- 
culated from the following considerations: 

If / denotes the distance between the hole L and the plate P, 
and v the frequency of rotation of the latter about the 

27 1. Langmuir, Am. Inst. Electr. Eng. Trans. 32, 1921 (1913), also references given above. 

28 S. Dushman, Phys. Rev., 5, 223 (1915). 

29 L. Dunoyer, Les Idees Modernes sur la Constitution de la Matiere. p. 215 (1913). This 
article contains a very interesting discussion of low pressure phenomena, especially of 
Knudsen's work (see p. 31). 

3°Zeits. f. Physik, 2, 49; 3, 417 (1920). 
Sc. Abst. 24, 12, 544 (1921). 



SO Kinetic Theory of Gases 

axis passing through L, it is evident that during the time 
t in which the molecules pass from L to P, the latter will have 
moved forward a distance s, where 

5 = 2 tv I. v. T 

But if v = velocity of molecules, 
r = l/v 

Hence, s = 2 it v P/v 

Thus, the measurement of s gives a direct determination 
of v, the velocity of the molecules. 

Experiments with a silver-coated platinum wire gave 
results on the velocity of silver atoms which corresponded very 
closely with the values calculated by means of equation (5) . It 
will be observed that in the latter equation, the velocity depends 
upon the molecular weight. Stern has therefore pointed out that 
the above method may be applied to determine molecular weights 
in the vapor state. 

Laws of Molecular Flow 

It is evident from the preceding considerations that at very low 
pressures the rate of flow of gases through tubes or narrow aper- 
tures must be limited solely by the frequency with which the 
molecules strike the walls of the tube or aperture and may thus 
be thrown back in the direction of incidence. At higher pressures 
the rate of flow of gases through narrow tubes is governed by 
Poiseuille's law. If Qi denotes the amount of gas (measured in 
terms of P. V) which flows per second through a tube of diameter 
D and length /, and rj denotes the coefficient of viscosity, Poi- 
seuille's law may be expressed by means of the equation, 

_ D*(P r -P 1 )P (27) 

Ql ~ 128 t,l (27) 

where P is the pressure at which Q is measured and P2-P1 
denotes the difference in pressure at the two ends of the tube. 
At very low pressures this relation is no longer valid, and for a 
reason which is self-evident. At ordinary pressures the rate 
of flow of gases must be limited by the frequency of collisions 
between molecules, hence the necessity for introducing the co- 
efficient of viscosity in the formula for the rate of flow. At very 
low pressures, however, where the length of L, the mean free 
path, is much greater than that of D, it is meaningless to speak 
of a coefficient of viscosity and it is therefore necessary to dis- 
card the hydrodynamical equations upon which Poiseuille's 
relation is based, in order to arrive at a more accurate relation 






Kinetic Theory of Gases 31 

for the rate of flow of gases through tubes. A similar difference 
has been observed for the laws of heat flow in gases at low and 
high pressures. For pointing out the manner of attacking both 
these problems and deducing a number of relations which are 
applicable to gases at low pressures, we are indebted to the theo- 
retical and experimental investigations of M. Smoluchowsky, M. 
Knudsen, and W. Gaede, who, since 1908, have published a large 
number of papers dealing with this subject.* 

The term "molecular flow" was suggested by Knudsen 31 to 
designate the condition of gases flowing through tubes at such 
low pressures that collisions between the molecules are infre- 
quent as compared with collisions at the walls. As has been 
shown, at these pressures L is much greater than D and 

the ratio -= increases with decrease in pressure, so that any mole- 
cule striking the inner surface of the tube at any point is repelled 
all the way across the tube until it strikes the opposite wall. 
Knudsen now assumes that any plane surface, no matter how 
smooth it may appear, consists in reality of toothlike projections 
which are probably due to one or more atoms being irregularly 
piled up above the surrounding atoms; that is, these projections 
are of molecular dimensions, and they are irregularly distributed 
over the surface. Consequently, "a gas molecule on striking 
the surface is repelled in a direction which is totally independent 
of the direction of incidence, and the distribution of directions 
of an infinitely large number of molecules after reflection from 
a surface follows Lambert's cosine law for the reflection of light 
from a glowing body. " 

Introducing Maxwell's distribution law and Meyer's equation 
for the number of molecules in a gas at rest that strike unit area, 
Knudsen arrives at the following relations for the case in which 
the diameter of the tube or aperture is infinitesimally small as 
compared with the length of the mean free path. 

In the case of a circular tube of diameter!}, and length/, the 
quantity of gas, Q 2 , which flows through per second, with a 
difference of pressure P 2 -P\, is given by the equation, 

Q 2 = |FA (28) 

* This subject is discussed at greater length in Chap. VI, and also in connection with 
the theory of the molecular gauge (p. 101). 

3i Ann. Phys. 28, 75, and 28, 999 (1908). Abh. Bunsenges. 3, 103 (1914). Also M. L. 
Dunoyer, loc. cit. 



32 



Kinetic Theory of Gases 



where 



w 6/ 

W\ = —7= = 



2.394 / 



(29) 



V2tt D* D* 

and pi denotes the density at 1 bar pressure and the temperature 
of the tube. 

From the gas laws it follows that, 

M 

Pl ~83.15X10 6 T 

It will be observed that equation (28) is analogous to Ohm's 
law, so that we may speak of the term Wi\/pi as the resistance 
to flow of the tube at the temperature T for a given gas. For 
different gases, the value of the resistance varies as the square 
root of M. 

For the case of a circular opening in a thin plate, equation (28) 
is still valid, but the value of W is given by the equation, 

where A is the area of the opening, and D its diameter. 

Hence where we have a tube of diameter D and length / con- 
necting two vessels at low pressures, the total resistance to flow, 
of this tubing, is 

_ Z2.394 I , 3.184\ - , N 

WPi = (^-5r-+-cirJ\/Pi (3D 

By means of these equations it is possible to calculate 
the quantity of gas that can flow through any given tube or 
opening at low pressures. The value of Q is obtained in terms of 
P V, that is, the volume in cm. 3 at a given pressure P, in bars. 

TABLE VI 

RATE OF FLOW OF AIR AND HYDROGEN AT LOW 

PRESSURES AND 20 DEG. C. 



1 


D 


W 


PFftCAlr, 


?£*<**■> 


1 cm. 
10 

1 
10 


1 cm. 
1 

0.1 
0.1 


5.578 
27.124 
2712.4 
24258.4 


5204. 
1070. 
10.70 
1.196 


19710. 
4053. 
40.53 
3.60 



As an illustration of the application of the above equation, Table 
VI gives the volume (in cubic cm.) of air or hydrogen (at 1 bar 
pressure) that would flow through different sizes of tubing for 
a difference of pressure of 1 bar, and room temperature. For 



Kinetic Theory of Gases 38 

air at 293 deg. abs, and 1 bar pressure, p x = 1.189 X10~ 9 and for 
hydrogen, under the same conditions, pi = 8.271 X 10~ n . 

From equation (31) and the data in Table VI it is evident that 
for long tubes of very small diameter (capillaries) the end cor- 
rection is negligible. The values of Qi for air and hydrogen may 
then be derived from the data in the table for I = 10 and D = 0.1 
by applying equation (29). 

These examples illustrate the effect of narrow tubes on the 
rate of exhaust at low pressures, and it is therefore absolutely 
essential that in experiments at low pressures where maximum 
speed of exhaust is desired, the connecting tubing should be as 
large in diameter as practicable, and also as short as possible. 

Laws of Flow at Higher Pressures 

The equations given above are strictly accurate only at such 

low pressures that y- is infinitesimally small. Actually it has 
been found by Knudsen that the equations are accurate to within 
5 per cent even at pressures where -=■ = 0.4. For air at room tem- 
perature and 1 megabar, the value of L is 9.4 X10~ 6 cm., and at 

9 4 
a pressure P (bars) L,=^ L . So that in case of a tube 1 cm. in 

diameter, the equation for molecular flow would be accurate to 
within 5 per cent for all pressures below about 3.76 bars. 

It is of interest in this connection to discuss briefly the manner 
in which the rate of flow of gas through a tube varies at higher 

pressures. If we denote the ratio, , D ~ 2 , by F, it is evident 

from the above discussion that for very low pressures this ratio 
is constant for any given gas and independent of the pressure. 
As, however, the pressure is increased the value of F is 
observed to decrease at first until it reaches a minimum value 
which is about 0.95 of its value at very low pressures. As the 
pressure is increased still further, F increases and the rate of 
increase with pressure is given by Poiseuille's law. From ex- 
periments over a large range of pressures with different gases, 
Knudsen has derived the following semi-empirical relation which 
is found to hold at all pressures: 

F = aP+b ^) (32) 

where, 



34 



Kinetic Theory of Gases 



a = 



b = 



C\ = 



IT D* 

128 rjl 
1 

VpiD 
V 



(Poiseuille's constant) 

(Coefficient of molecular flow) 

A 1.2Vpj D 
and c 2 = 



For ordinary pressures this equation assumes the form already 
given for Poiseuille's law, equation (27), while at very low pres- 
sures it becomes identical with equation (28). In order to illus- 
trate the application of equation (32) and also show the effect 
of pressure on the rate of flow of gases it is of interest to calculate 
by means of this equation the value of F at different pressures 
for air flowing through a tube 10 cm. long and 1 cm. in diameter, 
at room temperature. In Table VII, F expresses the volume in 
cubic cm., measured at 1 bar pressure and room temperature 
that flows through the tube for a difference of pressure of 1 bar 
at the ends and an average pressure of P bars. 

TABLE VII 

RATE OF FLOW OF AIR AT DIFFERENT PRESSURES 



P (bars) 


F (equation 32) 


F-1070 


10* 


13.56 x 10° 


13.56 x 10 6 


100 


2227 


1157 


50 


1555 


485 


20 


1160 


90 


10 


1058.1 


—11.9 


5 


1025.7 


—44.3 


4 


1023.6 


—46.4 


3 


1025.2 


—44.8 


1 


1043.6 


—26.4 


0.1 


1065.4 


— 4.6 


0.01 


1069.6 


— 0.4 



a = 135.6 



fc = 1070 



= 0.19033 



a = 0.2360 



These results have been plotted in Fig. 3. Itisseentha the 
minimum value in F occurs at about 4.5 bars. Even at this 
pressure the difference between the value calculated by means 
of equation (32) and that calculated by applying the simple 
equation (28) combined with equation (31) is less than 5 per cent 
of the value, F= 1070, calculated by the last mentioned method. 
Table VII also shows that the resistance of tubes is very much 
greater at extremely low pressures than at ordinary pressures. 



Kinetic Theory of Gases 



35 



Thermal Molecular Flow 32 

If two vessels at different temperatures are connected by a 
capillary tube, it is observed that at low pressures (where L is 
greater than D), there is a flow of gas from the colder to the 
hotter chamber until a pressure is established sufficient to check 



/072t 



J068 



>064 ■ 



/O60- 
1056 
J052 
/048- 



/044 

\ 

1040 
1036 

■toii 

1028 
1024 



III 

liHIHHI 



/ 2 3 4 5 6 7 8 9 JO 

Fig. 3 

it. For small differences in temperature, the pressure difference 
varies directly as the pressure and inversely as the temperature. 
It is also independent of the nature of the gas. The condition of 
equilibrium of pressures in the two parts of the svstem is then 
given by the relation : 

|l=Jp or £l = Jp (33) 

As the pressure is increased, the pressure difference rises less 
rapidly and finally reaches a maximum value. It then decreases 
and at higher pressures varies inversely as the pressure and also 
inversely a s the density of the gas. Under these conditions there 

*, 'o^- /?^ dsen ^ nn - Phys " 31 ' 205 and 33 - 1435 ( 19 ^0); G. D. West, Proc. Phys. Soc. 
V ? (1919)- The latter gives a critical discussion of the laws of thermal transpiration 
at both low and medium pressures. 



36 



Kinetic Theory of Gases 



is a flow of gas from the cold to the hot vessel along the surface of 
the tube and in the reverse direction along the axis. The con- 
dition for equilibrium at ordinary pressures is 



Pl = P 2 or «*-£ 

P2 1 1 



(34) 



Equation (33) is applicable to experiments at low pressures 
where different parts of a system are maintained at different 
temperatures. A usual case is where an appendix or trap con- 
nected with the vessel to be exhausted is kept immersed in liquid 
air (T = 80 approx.), while the pressure in the system is deter- 
mined by some form of sensitive gauge. Assuming that the 
latter is at room temperature (T = 298) ; it follows that the 
pressure in the part of the system immersed in liquid air is 

80 



V 



298 



= 0.52 of that read by the gauge. 



CHAPTER II 
HIGH VACUUM PUMPS 

Classification of Methods for the Production of Low Pressures 

The methods for the production of low pressures may be 
classified conveniently under the following headings : 

I. Mechanical Pumps 

1. Piston pumps 

2. Toepler and Sprengel mercury pumps 

3. Rotary mercury pumps 

4. Rotary oil pumps 

5. Gaede "Molecular" pump 

II. Mercury Vapor Pumps 

1. Gaede ' 'diffusion" pump 

2. Langmuir condensation pump 

III. Physical-Chemical Methods 

1 . Charcoal or other absorbing agent at low temperature 

2. Clean-up of residual gases by chemical reactions 

3 . Clean-up of gases by ionization methods 

General Theoretical Considerations Regarding Vacuum Pumps 1 

In comparing vacuum pumps it is necessary to consider the 
following factors, which are the main characteristics of a pump : 

1 . Exhaust Pressure. This is the pressure against which the 
pump may be operated. In general, the higher the degree of 
vacuum desired on the "fine" or intake side of the pump, the 
smaller the exhaust pressure should be. The low exhaust pres- 
sure is then obtained by means of another (so-called "rough") 
pump in series with the high vacuum pump. Two or more rough 
pumps may be used in series in order to obtain a sufficiently low 
exhaust pressure for the fine pump. 

2. Degree of Vacuum Attainable. "This is the lower limit of 
pressure which may be attained in a closed vessel connected to 
the pump. With most types of pump the degree of vacuum 
attainable depends to a large extent on the exhaust pressure 
used. This is usually due to leakage through the pump." In 
the case of the mercury vapor pumps, there is theoretically no 
lower limit to the pressure which may be attained, while in that of 
the Gaede molecular pump the limiting pressure bears a con- 
stant ratio to the exhaust pressure. 

1 In writing this section, the author has made extensive use of the article by Dr. Langmuir 
on "The Condensation Pump," in the General Electric Review, Dec, 1916, p. 1060. 



38 



High Vacuum Pumps 



3. Speed of the Pump. The law for the rate of decrease in 
pressure in a closed vessel connected to a pump is quite similar 
to that of chemical and physical reactions of the first order. 

It may be stated as follows : If p denotes the lower limit of 
pressure attainable with the pump, then the rate of decrease in 




Fig. 4. Geryk Vacuum Pump, Power Drive 



pressure at any instant is proportional to p 
the pressure at that instant. That is, 

dp 



dt 



= k(p-p ) 



po, where p denotes 



(35a) 



where k is a constant. Further consideration shows that with 
a given pump the rate of exhaust must vary inversely as the 
volume (V) of the vessel to be exhausted. Thus we can write 

-f = §(*>-/>») (35b) 

where 5 is a constant for the given pumping system, that is, 
pump and connecting tubing. Integrating the last equation we 
obtain the relation, 



c V i 
S=—ln 



\p2 — poJ 



(36) 



High Vacuum Pumps 89 

where t is the interval of time required to reduce the pressure 
in the volume V, from pi to p 2 . 

Gaede 2 has defined 5 as the speed of the pump, and it is ordi- 
narily measured in cubic cm. per second. It is readily seen 
that from the above equation 5 may also be defined as follows : 

With a pump of speed 5, it is possible to reduce, in each 
second, the pressure in a volume S cm. 3 by 63.2 per cent of the 
maximum possible decrease in pressure. It is necessary to distin- 
guish between the speed as defined in this manner and the actual 
speed of exhaustion, which we may denote by E. The latter is 
defined thus : 

dp E 

or 

t p2 

It is only when p = 0, that S and E are identical, and remain 
constant during the whole period of exhaust. In all other cases the 
speed of exhaust gradually decreases and as the pressure in the 
vessel approaches the limiting pressure, p , E decreases rapidly 
until it becomes zero when the pressure has decreased to p Q . 

The actual speed of exhaust depends not only upon the design 
of the pump but also upon the diameter and length of the con- 
necting tubing between pump and vessel to be exhausted. The 
pump and tubing together really constitute a system which is the 
equivalent of a pump of lower speed. Mention has been made 
in Chapter I of the results of Knudsen's investigations on 
the resistance to flow in tubes. According to these results, the 
quantity of gas, Q, flowing through a narrow tube is given by the 
relation 

o-^S (28) 

where W\/ Pl is the "resistance," and pi — pi is the difference in 
pressure at the ends. As in the previous chapter we shall write 

F=— — =— !— : (38) 

p2~pi VV\/pi 

Let us now assume that the volume of the tube is negligible 
compared to the volume of the vessel to be exhausted, and that 
the limiting pressure for the pump, po = 0. Let p 2 denote the pres- 
sure in the vessel and pi the pressure at the pump intake (end 
of the tube). Also let Si denote the speed of the pump itself, 

*Ann. Phys. 41, 337 (1913). 



40 High Vacuum Pumps 

and 5 2 the speed of pump and connecting tubing. Then since the 
quantity of gas taken out each second by the pump is the same 
as that flowing through the tube, we have the following relations : 
Q = F(p 2 -p 1 )=S 1 p 1 = S 2 p2 
Eliminating pi and pi from these equations, we obtain the 
equation, 

jrk +1 F . (39) 

which shows the effect of the added resistance of the tube on the 

speed of the pumping system. It will be observed that ~ has 

the same dimensions as W\/"^ (or 1/F), that is, the speed of a 
pump may also be looked upon as the reciprocal of a resistance to 
flow of gases through it, and by analogy with electrical usage we 

may define «- as the "impedance" of the pump itself and ^- as 

O] O2 

the impedance of pump and tubing. Similarly we may regard 
Si, S 2 and F, as "admittances. " 

It follows logically from these considerations that "in oper- 
ating vacuum pumps of high speed it is essential to use tubing 
of large diameter (and short length) between the pump and the 
vessel to be exhausted if full advantage is to be taken of the 
speed of the pump. " As an illustration of the effect of narrow 
tubes in diminishing the effective speed of a pump, let us consider 
the case of a tube 10 cm. long and 1 cm. diameter connected 
with a pump of speed Si =1400 cm. 3 per second (which is the 
value for a molecular pump under ordinary operating conditions) . 

The " resistance "of such a tube has been calculated in the pre- 
vious chapter. For air at room temperature 1 / W\/ pi = F = 1070. 
Applying equation (39) it follows that S 2 = 606, that is, the speed of 
the pumping system is about 43 per cent of that of the pump alone. 

With a pump which has a speed of 4000 cm. 3 per second (such 
speeds are easily attainable with mercury vapor pumps) the same 
piece of tubing would diminish the actual speed of exhaust to 844 
cm. 3 per second. In order to make effective use of the speed of 
this pump, it would be necessary to use very much larger tubing. 
Thus, let us assume that the connecting tube has a diameter of 
3 cm. and a length of 30 cm. (To use tubing larger than this is 
usually impracticable, while the length given is about as short 
as would be practical.) 

WV7>10- 4 X1.04 (for air at 20°C.) 

1/5, = 10-4x2.5 

Hence, So = 2825 cm. 3 per second. 



High Vacuum Pumps 



41 



These results indicate how seriously the speed of a mercury 
vapor pump may be limited by the resistance of the tubing 
unless this is of very large size. It also follows from these 
considerations that in the case of a low speed pump such as the 







Fig. 5. Details of Construction of Geryk Vacuum Pump 



High Vacuum Pumps 






Gaede diffusion pump (5 = 80) or a rotary oil pump (S=100), 
the resistance of the tubing, as long as it is not too large, is not 
nearly as important a factor as in the case of high speed pumps. 




Fig. 6. Gaede Piston Pump 



MECHANICAL PUMPS 

The early forms of exhaust pumps were of the piston type. 
As they have been largely superseded in modern practice, espe- 
cially for high vacuum work, no detailed mention of them need 
be made in this connection. Moreover, they are described in 
most elementary text-books on physics. 

Geryk Vacuum Pump 

This is a modern form of the piston type of pump (see Figs. 4 
and 5), made by the Pulsometer Engineering Co. The illustrations 



High Vacuum Pumps j^S 

and the following description are given by E. H. Barton: 3 
"Referring to Fig. 5, A is the suction pipe, B the air port 
into the cylinder above the piston, C is the piston whose bucket 
leather is kept up to the cylinder wall by oil pressing in the 
annular space D, E is the piston valve, F an air pipe to relieve 
the piston on the first few strokes, G, H and I collars and cover 
forming a good joint and delivery valve combined. 

"When the piston is at the bottom of its stroke as shown, 
there is a perfectly free opening from A to B. As the piston rises 
the port B is cut off and the cylinder full of air irresistibly car- 
ried up to outlet valve G. No air can get back past the piston 
as it is covered with oil. When the piston approaches the top of 
its stroke, it lifts the valve G off its face and gives a free outlet 
for the air. The oil on the piston then mingles with that shown 
above G, but the right quantity returns with the piston on the 
closing of G. L is the plug for filling up with oil, which is very 
non-volatile, moistureless and non-solvent of air and fills all clear- 
ance spaces and seals the valves. " 

With a single-cylinder pump of this type it is claimed that a 
pressure of about a quarter of a millimeter of mercury can readily 
be obtained. 

Gaede's Piston Pump 4 

This form, shown in Fig. 6, consists really of three piston 
pumps in series. The vessel to be exhausted is connected at 
R. As the piston rod D moves upwards, it carries with it the 
three pistons A, B, and C. The air is thus forced from N 
(which communicates with the tube M) through the valves O in 
the stationary partitions c, b, and a into the chamber K from 
which it is ejected into the air by the vent q. The top chamber 
K also contains a small amount of oil which forms an emulsion 
with the water and other vapors condensed above the piston A. 
"This emulsion is forced, together with the air, through the 
valve o in the cover a, through the tube P above the valve, and 
thence into the chamber K. This chamber is filled with a 
fibrous mass by which the oil and water emulsion is separated into 
its components. In consequence of its greater density, the water 
collects on the bottom M of the chamber, and may be pumped 
off as often as necessary by means of a glass syringe and rubber 
tube connected to the tube N extending upwards out of the pump. 

8 An Introduction to the Mechanics of Fluids, p. 197 (Longmans, Green & Co., 1915). 
See also Encycl. Britannica, 11th Edition, Vol. 22, p. 646. 
* W. Gaede. Phys. Zeits. H, 1238, 1913. 

See also E. H. Barton, loc. cit. pp. 198-9, from whose book the description given in the 
text is quoted. 






4.4 High Vacuum Pumps 

The oil overflows through the tube S into the space between a 
and M, whence it re-enters the pump barrel to combine with 
fresh quantities of water vapor. ' ' 

According to Gaede's published account it is possible with 
this pump to obtain a pressure as low as 0.00005 mm. mercury; 
i.e. 0.067 bar., when exhausting into atmospheric pressure. 

Sprengel Pump 

The use of a water- jet as a suction pump is quite familiar. 
With this pump, the minimum pressure obtainable is that corre- 
sponding to the vapor pressure of water at the temperature which 
it has in the supply line; i.e., from 5 to 10 mm. mercury. As the 
vapor pressure of mercury at ordinary temperatures is only about 
1 to 2 bars it is possible by means of a stream of mercury to 
obtain fairly low pressures, and by interposing a refrigerating 
chamber between the vessel to be exhausted and the nozzle 
which communicates with the mercury stream it is possible to 
obtain still lower pressures. The Sprengel mercury pump oper- 
ates on this principle, and some of the simpler forms are described 
in most elementary text-books. 5 

G. W. A. Kahlbaum 6 has described a form of Sprengel pump 
which he states to be capable of exhausting a 400 cubic cm. 
bulb in 30 minutes to 0.004 bar. In a subsequent paper 7 he gives 
the following data with regard to the speed of exhaust of a 500 
cubic cm. bulb: 

3 minutes to 0.5 mm. mercury 
15 minutes to 0.000165 mm. 
30 minutes to 0.000069 mm. = .092 bar 

He states that with special care he was able to get a pressure 
as low as .0024 bar. This pressure is evidently that of residual gas 
and does not include the pressure of the mercury vapor itself, 
which, as stated above, would be between 1 and 2 bars. 

Geissler-Toepler Pump 8 

The principle of this pump is fundamentally the same as that 
used by Torricelli in his famous experiment. In this type (Fig. 7) 
mercury forces the piston and also opens and closes certain ports, 
so that no valves are needed except one rough glass valve (g) to 

6 See Encycl. Brit. loc. cit., also Winkelmann, Handbuch der Physik. I, 2, pp. 1314-1332, 
contains a very detailed description of the different forms of Sprengel and Toepler mercury 
pumps. 

6Wied. Ann. 58. 199 (1894). 

7 See also L. Zehnder, Ann. d. Phys. 10, 623 (1903), for a description of an improved 
form of Kahlbaum's pump. 

8 See Encycl. Britannica and Winkelmann, loc. cit., also Barton loc. cit., from whose 
book Fig. 7 is taken. 



High Vacuum Pumps 




Fig. 7. Toepler Pump 

prevent the mercury from entering the vessel, E, which is being 
exhausted. The essential parts of the pump are made of glass 
and the air from E is exhausted by alternately raising and lowering 
the mercury reservoir R which is connected to the tube of baro- 






46 High Vacuum Pumps 

metric length below B. At each upward ''stroke,' ' the gas in B 
is closed from E and forced through the tube F, into the atmos- 
phere at M. Then on the downward stroke, the pressure in E 
is lowered by expansion of the gas into B. E. Bessel-Hagen 9 
has described a modified form of Toepler pump with which he 
claims to have obtained pressures of residual gas as low as 0.016 
bar. 10 Both the Sprengel and Toepler pumps have rendered very 




Fig. 8. Gaede Rotary Mercury Pump 

useful service in high vacuum investigations, and there is no doubt 
that with care it is possible to obtain pressures as low as .02 to 
.01 bar by their use. 

The great disadvantages of these pumps are, however, two- 
fold. First, they require constant personal attention during the 
exhaust and second, the speed of exhaust is extremely slow, as 
it depends upon the rate at which the mercury can be raised and 
lowered alternately. It is of interest to note in this connection 
the results obtained by Scheele and Heuse 11 in their investigation 
of the degree of vacuum attainable with different types of pump. 
They used a 6 liter bulb and measured the speed of exhaust by 
means of a very sensitive McLeod gauge.* In the experiments 

'•Wied. Ann. J*. 425. 1881. 

10 Other forms of Toepler pump are described by a A. Stock Ber. deutsch. chetn. (>es. 
88. 2182, 1905, and E. Grimsehl, Phys. Zeits. 8, 762, 1907. 

11 Zeits./. Instrumentenkunde, 29, 47, 1909. 

* See Chapter III for description of this gauge. 



High Vacuum Pumps Jfi 

with a Toepler pump, each stroke actually required two minutes, 
and tw T omore minutes were allowed between each stroke for equal- 
ization of pressure. Table VIII gives the pressures at the end of 
different intervals of time. 

The last column gives the "speed of exhaust " as calculated 
by equation (37). Compared with the speed of even 100 
cm. 3 /sec. obtained by a Gaede rotary mercury or an ordinary 
oil pump (described later) the speeds given in Table VIII are 
manifestly very low. Considering, furthermore, that in the 
case where gas is continually evolved from the walls, the min- 
imum attainable pressure is given by the ratio S/q where q 
denotes the rate of gas evolution, it is seen that in actual practice 
it would be very difficult to obtain pressures below .01 bar by 
means of a Toepler pump. 

Similar results were obtained by Scheele and Heuse in investi- 
gating the rate of exhaust of a 6 liter bulb by means of a Sprengel 
pump (Zehnder's form). 12 

TABLE VIII 
SPEED OF EXHAUST WITH TOEPLER PUMP 



t 


press 




2.3 V pi 

E= "60T log p! 


(minutes) 


(mm. Hg.) 



2 


0.0645 
0.0399 1 


j 


0.40 


24 


0.0254 f 




0.38 


48 


0.0107 


1 


0.35 


60 


0.00709 


J ■ 


108 


0.00141 


1 




120 


0.00093 




0.35 


180 


0.00024 




0.39 


192 


0.00015 




240 


0.000053 




0.28 


252 


0.000038 


f 


264 


0.000032 


1 


0.06 


300 


0.000025 


J 



Gaede Rotary Mercury Pump 

An automatic form of Toepler pump has been described by 
U . von Reden, 13 with which he claims to have exhausted a 500 cm. 3 
bulb in 13 minutes to a pressure of .00001 mm. From his data, 
the speed of exhaust is found to be about 20 cm. 3 /sec. In 1905, 
W. Gaede designed a rotary mercury pump which has been used 
to a very large extent in the commercial exhaust of incandescent 

'= Ann. d. Phys. 10, 623 (1903). 
» Phys. Zeits. 10, 316, 1909. 



4S 



High Vacuum Pumps 



lamps and Roentgen tubes until quite recently. The pump as 
described in the first publication 14 and illustrated in Fig. 8, consists 
of an iron casing (with glass front) partially filled with mercury, 
in which a porcelain drum is made to rotate. A rough pump 
producing a vacuum of 10 to 20 mm. is used as fore-pump. 
Fig. 9 shows a vertical section of the pump, and Fig. 10 a front view. 
The iron case is shown at g, and G is a heavy glass plate through 
which pass the tubes R and r which connect to the vessel to be 









X 

g ! 














r i 




q 




g 


t 




f L w,.j t 


s 


"R J 


4 : 

! t 
U 


_a 


g 


t 






g 


























g i 







Fig. 9. 



Gaeda Rotary Mercury Pump, 
Vertical Section 



exhausted and the fore-pump respectively. The porcelain 
drum t is built up of two (or more) sections as shown in Fig. 9 
and rotates on the axis a. As the drum rotates in the direction 
of the arrow the compartment W is at first increased in volume 
and thus sucks in the gas at the opening/, from the vessel to 
be exhausted. During the second part of the revolution, the 
opening / becomes covered with mercury, as shown at/2, and the 
gas is then forced out under pressure from the compartment Wi 
into the space between the walls Z\ and U and into the rough 
pump connection at P. 

Fig. 11 shows an improved form of the pump in which the 
opening to the rough pump r is brought in through the iron casing. 
The vessel to be exhausted is connected at E, and a side tube t 
is provided with P 2 5 to take up water vapor. The tube MOF 
acts as manometer and also makes it possible to exhaust with 

w Verh. d. deutsch. Physik. Ges. 7, 287, (1905). Phys. Zeits. 6, 758-760 (1905). 



Hi^h Vacuum Pumps 



49 



the rough pump alone at the beginning. As the vacuum im- 
proves, the mercury in o rises and seals off the connection to the 
rough pump through a Sv The system is then ready for exhaust- 
ing to lower pressure by means of the mercury pump. 

Table IX gives data for the speed of exhaust of a volume of 
6250 cm. 3 with a Gaede rotary pump operating at 20 r.p.nl. 

TABLE IX 
SPEED OF EXHAUST WITH ROTARY MERCURY PUMP 



t (mm.) 


P (mm.) 


„ 2.3 V Pi 

E= i6or log ir 







9 




5 




0.03 


94.5 


10 




0.0018 


46.5 


15 




0.00023 


34.0 


20 




0.0001 


13.8 


25 




0.00007 


6.9 


30 


* 


0.00007 


0.0 




Fig. 10. 



Gaede Rotary Mercury Pump, 
Diagrammatic View 



The speed of this pump is therefore approximately 100 
cm. 3 /sec. at the maximum, while the degree of vacuum attain- 
able is about .00007 mm. or 0.1 bar. 15 

Rotary Oil Pump 16 

Figs. 12 and 13 show the construction of a pump of this type 
designed by Gaede primarily for the purpose of acting as a fore- 

16 Later improvements in this pump have been described in Verh. d. deutsch. Physik. 
Ges. 9, 639 (1907). and Phys. Zeits 8, 852 (1907). 

>• G. Meyer, Verh. d. deutsch Phys. Ges. 10, 753 (1907). 



50 



High Vacuum Pumps 



pump to the rotary mercury pump just described. It is also 
shown in Fig. 16 at the right hand side. The pump consists of 
a steel cylinder A which rotates eccentrically inside a steel casing. 
The projections at S are held tightly against the inner wall by 
means of springs, so that as the cylinder rotates the air is sucked 
in at C and forced out through the valve D into the oil chamber 
and from there into the atmosphere at J. The oil serves as 



tlso 




Fig. 11. Improved Form Gaede Mercury Pump 

automatic lubricant and also helps to prevent air from leaking 
back into the fine pump side, by forming a film between the 
rotating and stationary members. 

Fig. 14 illustrates a standard form of rotary oil pump used in 
incandescent lamp factories and which can also be used as a fore- 
pump to higher vacuum pumps such as Gaede's Molecular or 
Langmuir's Condensation pump. With a fore-pump pressure 
of about 1 cm. mercury, such a pump is capable of exhausting 
to a pressure of approximately 1 bar, and with two pumps in 
series the fine side pressure may be lowered to 0.1 bar. 17 

"K. T. Fischer. Verh. deutsch. Physik. Ges., 7, 383 (1905), has described a form of rotary 
oil pump for use in commercial exhaust operations. With two pumps in series exhausting 
into atmospheric pressure he states that a pressure of about 2 bars may be obtained. 



High Vacuum Pump* 



51 



With a pump of this type operating at about 400 r. p.m., 
the speed of exhaust is 100-150 cm. 3 per second. 

Gaede Molecular Pump 

The Gaede molecular pump undoubtedly marks a distinct 
advance in the design of pumps for the production of high 
vacua. The difference between this pump and the types 
previously constructed has been well described by Gaede himself 
in the paper which he published in 1913 : 18 




Fig. 12. Gaede Rotary Oil Pump, Side View 



' ' All high vacuum pumps known up to the present consist of 
an exhaust arrangement which, according to the original idea 
of Otto von Guericke, separates a definite volume of gas from 
the vessel to be exhausted, and then gives it up to a fore- vacuum 
or the atmosphere. It is absolutely essential in these pumps 
to separate the rough side from the higher vacuum side as 
much as possible. This is accomplished in the mechanical pumps 
by tight-fitting pistons and valves, and in the case of mercury 
and oil pumps by means of the liquids themselves. On the other 

« W. Gaede, The Molecular Air Pump. Ann. d. Phys. 41, 337-380 (1913). This paper 
contains a complete discussion of the theory and construction of the pump. Briefer 
descriptions may also be found in the following: 

W. Gaede. Physikal, Zeits. IS, 864-870 (1912), and Verh. d. deuts. Phys. Ges. 14. 
775-787 (1912). 

K. Goes, Physikal, Zeits. 13, 1105. and 14, 170-2 (1913). Description of some 
experiments with the pump and precautions in using it. 

Electrician (London), 70, 48-50 (1912). 

K. Jellinek, Lehrbuch d. Physikal, Chemie, I, 1, pp. 330-333 (1914). 

M. L. Dunoyer, 'Les Idees Modernes sur la Constitution de la Matiere. pp. 215-271 
(1913). 



52 High Vacuum Pumps 

hand, in the case of the molecular pump there is no separa- 
tion, whether piston or fluid, between the high-vacuum and fore- 
vacuum. " The gas is. dragged along from the vessel to be 
exhausted into the fore-vacuum by means of a cylinder rotating 
with high velocity inside a hermetically sealed casing. The 
pump thus represents a logical development and application 
of the laws of flow of gases at very low pressures as investigated 
by Knudsen, Smoluchowski, and Gaede himself. 



Fig. 13. Gaede Rotary Oil Pump, Front View 

The fundamental principle of the pump may be illustrated by 
means of Fig. 15. The cylinder A rotates on an axis a (in the 
direction of the arrow) inside the air-tight shell B and drags the 
gas from the opening n towards the opening m, so that a pressure- 
difference is built up in the manometer M, as shown by the 
mercury-levels at o and p. Between m and n there is a slot in 
the case B as shown in the diagram, while at every other point 
A and B are very close together. Now, at ordinary pressures 
the viscosity is independent of the pressure. Under these 
conditions, as Gaede shows, the difference in pressure at o 
and p depends only on the speed of rotation u, of the cylinder, 
the coefficient of viscosity of the gas, n, the length of the slot, 
L and h the depth measured radially, according to the follow- 
ing relation: 

pi — p2 = 6 Lun/h 2 

At low pressures, however, the number of collisions between 
gas^molecules becomes relatively small as compared with the 



High Varum)! Pumpi 



58 




Fig. 14. Standard Form of 
Rotary Oil Pump 



z^rG=^\ m /pC^\ 




Fig. 15. Diagram Explaining Operation of Molecular Pump 



54 



High Vacuum Pumps 



number of collisions between the gas molecules and the walls. 
Under these conditions the molecules therefore tend to take 
up the same direction of motion as the surface against which 
they strike, if the latter is in motion. This conclusion is based 
upon the investigations of Knudsen on the laws of molecular 




Fig. 16. 



Gaede Molecular Pump, 
Front View 



flow, which have been discussed in Chapter I. The relation 
previously deduced is therefore found to be no longer true and 
instead of the pressure-difference remaining constant at con- 
stant speed of rotation, the pressure-ratio is now constant and 
independent of the pressure in the fore- vacuum. Gaede shows 
that at very low pressures, 

P 1 /P 2 = Ku 
where K is a constant whose value depends upon the nature of 
the gas and the dimensions of the slot in the casing B of the 
pump, so that at constant speed of rotation u, the ratio between 
the pressures on the two sides of the pump is constant. 

The construction of the actual pump based on these 
principles is illustrated in Figs. 16 and 17, while Fig. 18 shows 
the pump connected in series with a Gaede rotary oil pump. 



High Vacuum Pumps 



55 



The rotating cylinder A (Figs. 16 and 17) has 12 parallel slots 
around the circumference, into which project the extensions C 
from the outer casing. If A rotates clockwise, the pressure at m 
is greater than that at n, and in order to increase this pressure 
different sections are connected in series. The distance between 




Fig. 17. Gaede Molecular Pump, 
Side View 



the outer edge of the cylinder A and the inside of the shell B 
is about 0.01 cm. The over-all radius of A is 5 cm., and the 
depth of the slots varies from 0.15 cm. in the outer section to 0.6 
cm. in the inner ones. With the cylinder rotating clockwise 
as indicated, the vessel to be exhausted is connected at S, 
while the opening T is connected to an ordinary mercury or oil 
pump capable of exhausting to a pressure of less than 0.05 
mm. Hg. As the speed of rotation of the cylinder is very high 
(about 8000 r.p.m.) oil cups are provided at F, and the shaft N is 
so designed that the oil in the spiral slot is driven outwards 
by the centrifugal action. The slots in the rotor are so 
arranged that the lowest pressure is in the center, and the 
pressure increases uniformly outwards until the ends, where 
it is equal to that produced by the rough pump. 



High Vacuum Pumps 




Fig. 18. Assembly of Gaede Molecular and Gaede Rotary Oil Pumps 



The effect of varying the speed of rotation or the rough pump 
pressure on the degree of vacuum produced by the molecular 
pump, is shown in Table X. 

TABLE X 

EFFECT OF SPEED OF ROTATION ON DEGREE OF VACUUM 

OBTAINED WITH GAEDE MOLECULAR PUMP 



Speed of Rotation 


Rough-pump Press. 


Press, on Fine Side 


R.P.M. 


mm. Hg. 
0.05 


mm. Hg. 


12000 


0.0000003 


12000 


1 


0.000005 


12000 


10 


0.00003 


12000 


20 


0.0003 


6000 


0.05 


0.00002 


2500 


0.05 


0.0003 


8200 


0.1 


Not measurable 


8200 


1. 


0.00002 


8200 


10 


0.0005 


6200 


0.1 


0.00001 


6200 


1.0 


0.00005 


4000 


1.1 


0.00003 


4000 


1 


0.0003 



High Vacuum Pumps 57 

The pressures on the fine side were measured with an 
extremely sensitive type of McLeod gauge except in the case 
of the first result given in the table which was estimated. The 
writer's own experiments 19 with the Gaede molecular pump at 
8000 r.p.m. have shown that with a rough pump pressure of 
20 mm. the fine side pressure was 0.0004 mm., so that the ratio 
of the pressures was 50,000— a result which is in accord 
with figures given by Gaede. 




Fig. 19. Effect of Rough-pump Pressure on 
Speed of Gaede Molecular Pump 

The speed of the pump as defined by equation (37) has 
been found by Gaede to vary with the magnitude of the 
rough-pump pressure. The curve A in Fig. 19 shows that the 
maximum speed is about 1400 cm. 3 per second with a fore- 
vacuum of 0.01 mm. For comparison Gaede also shows the 
curve B for his rotary mercury pump, which has a speed of 
about 130 cm. 3 per sec, at the maximum. 



MERCURY VAPOR PUMPS 20 

The fact that a reduction in pressure can be obtained by a blast 
of steam or air has been known and applied in the industry for 
a long time. In steam aspirators or ejectors such as are used 
for producing the low pressure required in the condenser of a 

» S. Dushman, Phys. Rev. 5, 224 (1915). 

20 The introductory remarks are based largely upon the discussion of this subject by 
I. Langmuir in his paper on, "The Condensation Pump, an Improved Form of High 
Vacuum Pump," General Electric Review, 1916, p. 1060, also Journ. Franklin Inst.. 
182, 719 (1916), Phys. Rev. 8, 48 (1916). An excellent discussion of the mercury vapor 
pumps described in this section has also been written by A. Gehrts, Naturwissenschaften, 
7, 983 (1919>. 



58 



High Vacuum Pumps 



steam turbine, "the high velocity of the jet of steam causes, 
according to hydrodynamical principles, a lowering of pressure, 
so that the air to be exhausted is sucked directly into the 
jet." An analysis of the action of the aspirator shows, 
according to Langmuir, that in its action two separate 
processes are involved. 

"1. The process by which the air is drawn into the jet. 

"2. The action of the jet in carrying the admixed air along 
into the condensing chamber. 

B 




C 



\ 



D 



Fig. 20. Diagram Illustrating Principle of Diffusion Pump 



"The aspirators cease operating at low pressures because 
of the failure of the first .of these processes. If air at low 
pressure could be made to enter the jet, and if gas escaping 
from the jet could be prevented from passing back into the 
A^essel to be exhausted, then it should be possible to construct 
a jet pump which would operate even at the lowest pressures. " 

This problem has been solved in two different ways by 
Gaede and Langmuir. In the pumps devised by each of 
these, a blast of mercury carries along the gas to be exhausted 
into the condenser (process 2). In order to introduce gas 
into the blast of mercury, Gaede has used diffusion through 
a narrow opening. On the other hand, Langmuir has made use of 
the fact that the mercury atoms on colliding with the gas 



High Vacuum Pumps 39 

molecules must impart to the latter a portion of the momentum 
which they possess in virtue of their high average kinetic 
energy, while the mercury atoms themselves are removed 
rapidly from the stream of mixed gases by condensation on 
the cooled walls. 

Gaede's Diffusion Pump 21 

The action of Gaede's "diffusion" pump can best be illus- 
trated by referring to Fig. 20. A blast of steam is blown through 
the tube A B, in which is fixed a porous diaphragm C. The 
vessel to be exhausted is attached at E. Water vapor diffuses 
through the capillaries in the diaphragm into the trap D 
where it is condensed by some refrigerating agent, while air 
diffuses through the diaphragm in the opposite direction into 
the tube A B, from where it is drawn away rapidly by the 
blast of steam. The result is that the pressure in E decresses 
and finally reaches a very low value. 

A study of the phenomena of diffusion of gases through mer- 
cury vapor in narrow tubes led Gaede to the conclusion that at 
sufficiently low pressures, where the mean free path L of the 
air molecules in mercury vapor is comparable with the diameter 
d of the tube, the volume of air, V, diffusing through a tube of 
length /, per unit time, is given by relation of the form: 

V = kird 3 /l (40) 

where k is a constant for any given gas A. In other words, the 
speed of exhaust is independent of the actual pressure of the 
gas in the vessel to be exhausted, and the relative decrease in 
the pressure per unit time therefore remains constant as the 
pressure in the system is decreased. This result obtained 
empirically by Gaede is evidently in agreement with Knudsen's 
deductions as stated in equations (28) and (29), Chapter I. 

The actual construction of the diffusion pump is shown in 
Fig. 21. The porous diaphragm is replaced by a steel cylinder C 
with a narrow slit S whose width can be altered by means of 
the set screws H. The cylinder is set in the mercury trough G, 
which forms a seal between the low and high pressure parts. 
The mercury at A is heated and the stream of vapor passes over 
the slit in the steel cylinder in the directions indicated by the 
arrows. The air or other gas from the system to be exhausted 
(connected at F) diffuses into this mercury stream at S, and then 
passes out through E into the fore-pump which is connected at V. 
Any mercury vapor passing out through S is condensed on the 

« Ann. Phys. 1,6, 357-392 (1915). 



60 



High Vacuum Pumps 




jr& 



Fig. 21. Gaede Diffusion Pump 



glass in the immediate neighborhood, by means of the water 
cooling jacket Ki K 2 . The opening V connects with the fore- 
pump or other source of rough vacuum and is used for exhausting 
the system until the pressure gets low enough for the operation 



High Vacuum Pumpi 



61 



of the diffusion pump to become effective. As soon as this stage 
is reached the mercury in the trap automatically closes this 
opening and the exhaust then continues by means of the diffusion 
pump. 

According to Gaede's theory the maximum speed of the pump 
is attained when the width of the slit S is of the same order of 
magnitude as the mean free path of the gas molecules in the slit 



wo 










90 


- 




- 


80 


f\ 


10 


- / \ 


60 


- 


\ 


SO 


- 


N. 


40 




\. 


30 




^s. 


20 


- 


^V. 


10 


- 




1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -1 1. 



0.6 0.8 t.O t.Z r.+ /6 1.8 

Pressure of Mercury in m m. 



Fig. 22. 



Effect of Mercury Vapor Pressure on Speed of 
Diffusion Pump 



and when the vapor pressure of the mercury is only slightly 
in excess of the pressure in the fore-vacuum (at V) . Consequently 
the temperature of the mercury vapor has to be maintained at a 
fairly constant value. For this purpose a thermometer, T, is 
placed inside the tube B. 

The effect of varying the temperature of the vapor (and 
consequently its pressure) on the soeed of exhaust is shown by 
the data (given by Gaede) in Table XI and the plot of these 
in Fig. 22. These results were obtained with a slit width of 
0.012 cm. The maximum speed of 80 cm. 3 per sec. was attained 
at a temperature of the mercury vapor of 99° C. At this tern- 



High Vacuum Pumps 



perature the pressure of the mercury vapor is 0.27 mm., while 
the mean free path for air in mercury at this pressure according 
to Gaede's calculation is about 0.023 cm. 

Table XII shows the effect of varying the width of the slit. 
The noteworthy fact is that the speed of the pump remains 
constant as the pressure in the exhausted system is decreased, 
a result which Gaede previously deduced from theoretical 
consideration, as mentioned already. 

The great advantage of the diffusion pump over all the pre- 
vious types of pump consists therefore in the fact that there is 

TABLE XI 

EFFECT OF PRESSURE OF MERCURY VAPOR ON SPEED OF 
EXHAUST WITH DIFFUSION PUMP 



T 


P (mm.) 


S 


T 


P 


S 


y0°c. 


0.165 


13.4 


118.5 


0.72 


51 




94 


0.20 


60 


127.5 


1.10 


38 




97 


0.24 


70 


134 


1.51 


23 




99 


0.27 


80 


139 


1.84 


15 




113 


0.55 


62 


143.5 


2.2 


11 





theoretically no limit to the degree of vacuum which can be 
attained by its operation. In the case of the Gaede rotary 
pump and all mechanical pumps the speed of exhaust decreases 
with decrease in pressure. In the case of the Gaede molecular 
pump the minimum pressure attainable depends upon the 
pressure in the fore-vacuum as the ratio of the pressures 
is constant for the pump. There is thus with all these 
pumps a fixed lower limit to the lowest pressure attainable 
in the exhaust system. While there is no such limitation 
with the diffusion pump, it does have the double disadvantage 
of low exhaust speed and the necessity of carefully regulating the 
temperature of the mercury vapor. 

TABLE XII 

EFFECT OF WIDTH OF SLIT ON SPEED OF EXHAUST WITH 

DIFFUSION PUMP 



WIDTH OF SLIT =0.025 CM. 


WIDTH OF SLIT =0.004 CM. 


P 


5 


P 


5 


0.025 mm. 


77 


0.07 mm. 


52 


0.009 


72 


0.028 


48 


0.0025 


67 


0.006 


40 


O.OOOS 


72 


0.0015 


88 


0.0002 


73 


0.0004 


41 


0.00006 


70 


0.00007 


40 



High Vacuum Pumps 63 

Langmuir s Condensation Pump 

Both these disadvantages are removed in the type of mer- 
cury vapor pump designed by Langmuir, while the advantages of 
the diffusion pump are retained. In constructing and operating 
a pump of this type it occurred to Langmuir that "the limitation 
of speed could be removed if some other way could be found to 
bring the gas to be exhausted into the stream of mercury vapor." 20 
As stated previously, Langmuir comes to the conclusion that the 
ejector pump must become inoperative at low pressure, since 
at these pressures, "according to the kinetic theory of gases, 
the molecules in a jet of gas, passing out into a 
high vacuum must spread laterally, so that there would be no 
tendency for a gas at low pressures to be drawn into such a 
blast." 

Furthermore, under these conditions, the mercury atoms 
condense on the walls of the inner tube near the inlet and 
owing to the latent heat of evaporation raise the temperature 
of the walls so that condensation ceases, and the mercury 
atoms are merely reflected from the walls in all directions. 
Consequently there is just as much tendency for the mercury 
to diffuse back towards the exhaust system as away from it, 
and the air molecules are thus prevented from entering into the 
mercury blast at the nozzle. 

These considerations and the results of his previous investiga- 
tions on the mechanism of condensation of gas molecules on 
solid surfaces* led Langmuir to the conclusion that the mercury 
atoms could readily be prevented from diffusing back in the direc- 
tion from which the gas molecules are diffusing by simply cool- 
ing the walls of the tube near the mercury vapor outlet. Under 
these conditions the mercury atoms ought to be rapidly condensed 
as they strike the walls. At the same time the gas molecules dif- 
fusing in from the system to be exhausted would collide with the 
high speed mercury atoms at the jet and thus acquire a velocity 
component from the latter which would remove them rapidly 
from the space around the jet opening. The whole action of 
the pump constructed on the basis of this reasoning thus rests on 
the fundamental principle that the mercury vapor is rapidly 
condensed as it leaves the jet and the temperature is main- 
tained so low that the mercury does not re-evaporate to any 
measurable extent. Langmuir has therefore suggested that 
pumps based on this principle should be designated as "Conden- 
sation" pumps. 

* These investigations are discussed in Chapter VI. 



H 



High Vacuum Pumps 



A convenient type of glass condensation pump constructed 
on this principle is shown in Fig. 23. 

' ' In order that the pump may function properly it is essential 
that the end of the nozzle L shall be located below the level 
at which the water stands in the condenser J. In other words, 




Fig. 23. Langmuir Condensation Pump, Glass Form 



the overflow tube K must be placed at a somewhat higher 
level than the lower end of the nozzle as is indicated in the 
figure. The other dimensions of the pump are of relative unim- 
portance. The distance between L and D must be sufficiently 
great so that no perceptible quantity of gas can diffuse back 
against the blast of mercury vapor, and so that a large enough 
condensing area is furnished. 



High Vacuum Pumps 65 

"The pump may be made in any suitable size. Some have 
been constructed in which the tube B and the nozzle L were 
one and a quarter inches in diameter while in the other pumps 
this tube was only one quarter of an inch in diameter and the 
length of the whole pump was only about four inches. The larger 
the pump the greater is the speed of exhaustion that may be 
obtained. 

' ' In the operation of the pump the mercury boiler A is heated 
by either gas or electric heating so that the mercury evapo- 
rates at a moderate rate. A thermometer placed in contact with 
the tube B, under the heat insulation, usually reads between 
100 and 120 deg. C. when the pump is operating satisfactorily. 
Under these conditions the mercury in the boiler A evaporates 
quietly from its surface. No bubbles are formed, so there is 
never any tendency to bumping. 

"Unlike Gaede's diffusion pump, there is nothing critical about 
the adjustment of the temperature. With an electrically heated 
pump in which the nozzle L was J^ in. in diameter, the pump 
began to operate satisfactorily when the heating unit delivered 
220 watts. The speed of exhaustion remains practically unchanged 
when the heating current is increased even to a point where 
about 550 watts is applied. 

' ' The back pressure against which the pump will operate de- 
pends, however, upon the amount and velocity of the mercury 
vapor escaping from the nozzle. Thus in the case above cited, 
with 220 watts, the pump would not operate with a back pres- 
sure exceeding about 50 bars, whereas with 550 watts back pres- 
sures as high as 800 bars did not affect the operation of the pump." 

Condensation Pumps Built of Metal 

For most practical purposes a glass pump has many disad- 
vantages. Langmuir has therefore applied the same principles 
to the construction of a metal pump. 

One such type of pump which has proved relatively simple 
in construction and efficient in operation is shown diagrammati- 
cally in Fig. 24. "A metal cylinder A is provided with two 
openings, B and C, of which B is connected to the backing pump 
and C is connected to the vessel to be exhausted. Inside of 
the cylinder is a funnel-shaped tube F which rests on the bottom 
of the cylinder A. Suspended from the top of the cylinder is a 
cup E inverted over the upper end of F. A water jacket, J, 
surrounds the walls of the cylinder A from the level of B to a 
point somewhat above the lower edge of the cup E. 



66 



High Vacuum Pumps 



"Mercury is placed in the cylinder as indicated at D. By 
applying heat to the bottom of the cylinder the mercury is 
caused to evaporate. The vapor passes up through F and is 
deflected by E and is thus directed downward and outward 
against the water-cooled walls of A. The gas entering at C 
passes down between A and E and at P meets the mercury vapor 




Fig. 24. 



Diagram of Construction of Condensation Pump, 
Metal Form 



blast and is thus forced down along the walls of A and out 
of the tube B. The mercury which condenses on the walls 
of A falls down along the lower part of the funnel F and returns 
again to D through small openings provided where the funnel 
rests upon the bottom of the cylinder. A more detailed drawing 
of the pump as actually constructed is shown in Fig. 25." 

A pump in which the funnel F is 3 cm. in diameter and the 
cylinder A is 7 cm. in diameter gives a speed of exhaustion for 
air of about 3000-4000 cm. 3 per second. It operates best against 
an exhaust pressure of 10 bars or less and requires about 300 
watts energy consumption in the heater circuit. 



Degree of Vacuum Obtainable 

"The condensation pump resembles Gaede's diffusion pump 
in that there is no definite lower limit (other than zero) below 
which the pressure cannot be reduced. This is readily seen 
from its method of operation. A lower limit could only be 
caused by diffusion of gas from the exhaust side (N in Fig. 23) 



High Vacuum Pumps 



67 



back against the blast of mercury vapor passing down from L. 
The mean free path of the atoms in this blast is of the order 
of magnitude of a millimeter or less and the blast is moving 
downward with a velocity at least as great as the average molec- 
ular velocity (100 meters per second for mercury).* 




Fig. 25. Langmuir Condensation Pump, Metal Form 



' ' The chance of a molecule of gas moving a distance about 4.6 
times the mean free path without collision is only one in a 
hundred. To move twice this distance the chance is only 1 
in 100 2 , etc. If the mean free path were one millimeter the chance 
of a molecule moving a distance of 4.6 cm. against the blast with- 
out collision would be 1 in 10 20 . In other words, an entirely 
negligible chance." 

* This is apparent when we consider that no appreciable number of atoms pass up into the 
space E. 



68 



High Vacuum Pumps 



Actual observations with the ionization gauge* in this labo- 
ratory have shown that it is possible with the Langmuir conden- 
sation pump to obtain pressures which are of the order of 10 -4 
bar or less. The limiting factor which ordinarily makes it 
impossible to obtain pressures as low as this, is the continuous 
liberation of gas from the glass walls or metal parts, so 




Fig. 26. Condensation Pump, Arc Type 



that it becomes extremely difficult to obtain vacua in excess 
of the above order of magnitude. The necessary precau- 
tions in using the pump are discussed at greater length in 
Appendix I. 

Other Forms of Mercury Vapor Pumps 

Other forms of mercury vapor pumps have been described by 
H. B. Williams, 22 Chas. T. Knipp, 23 and L. T. Jones and N. O. 
Russell. 24 The construction used by the latter is shown in Fig. 
26. The advantage of this form is that it " permits using the 
pump as a mercury still at the same time that it is being used for 
exhaustion purposes. Two barometer columns introduce the 
mercury into the arc, the arc being started by blowing in one 
neck of the Woulff bottle. As shown at B the mercury vapor 
is driven through the nozzle N, and condenses in the chamber 
surrounded by the water jacket, J. The condensed clean mercury 
is then drawn off at O." With a current of 10-15 amps., a 
speed of exhaust of 400 cm. 3 per sec. was obtained. 

* See Chapter III for description of this gauge. 
« Phys. Rev. 7, 583 (1916). 
w Phys. Rev. 9, 311 (1917), and 12, 492 (1918). 
" Phys. Rev. 10. 301 (1916). 



High Vacuum Pumps 



69 



A simple construction for a condensation pump has also 
been described by W. C. Baker. 25 In this form as well as 
Knipp's the main object of the design is to simplify the glass 
blowing. 




Fig. 27. Crawford's Form 

of Condensation Pump, 

Vertical Type 



J. E. Shrader and R. G. Sherwood 26 have used a modified 
form of Langmuir condensation pump made of pyrex. Full 
details with all necessary dimensions are given in the original 
paper. The speed of the pump was measured for different 
amounts of energy input into the mercury heater and was 
found to be a maximum at about 400-500 watts input. With 

55 Phys. Rev. 10. 642 (1916). 
26 Phys. Rev. 12, 70 (1918). 



70 



High Vacuum Pumpi 






the speed of exhaustion purposely cut down by a special 
constriction, the maximum speed observed was around 225 cm. 3 
per sec. and pressures as low as 2X10 -8 mm. Hg were obtained 
after care had been taken to heat up all the glass parts to a tem- 
perature of 500° C. for a long time. 

An interesting form of mercury vapor pump is that devised by 
W. W. Crawford 27 and shown in Figs. 27 and 28. "The mercury 
vapor generated in the boiler B at a pressure of 10 mm. of 
mercury or more, escapes through the narrow throat T 




Fig. 28. Crawford's Form of Condensation Pump, 
Horizontal Type 



(Fig. 27), ahead of the point of entrainment. The vapor 
expands in the diverging nozzle N, and the issuing jet passes 
through the tube E, which it fills, and condenses in D, mostly, 
where it is found at the upper end. A slight amount of vapor 
escapes into the chamber A and condenses there. The con- 
densed vapor drains back through the tubes a and b, to the 
boiler. " The vessel to be exhausted is connected at c, while D 
connects with the rough pump. The speed of the pump in 
series with 10 cm. of tubing, 1.9 cm. in diameter was observed to 
be around 1300 cm. 3 per sec. at a boiler pressure of 10 mm. of Hg. 
A two-stage mercury vapor pump to work against a primary 
vacuum of 2 cm. given by a water aspirator, has been described 
by C. A. Kraus. 28 It consists essentially of two Langmuir con- 
densation pumps in series. The pump is very rapid and is 
capable of exhausting 1500 cm. 3 to less than 10~ 4 mm. in 10 min. 

« Phys. Rev. 10, 557 (1917). 

« J. Am. Chem. Sec. 39, 2183 (1917). 






High Vacuum Pumps 71 



H. F. Stimson has also constructed a two-stage pump along 
the same principles, 29 which is illustrated in Fig. 29. "The oper- 
ation of the pump is as follows : Cooling water entering at tube 
A flows up through the water jacket B above the lower end of 
nozzle F, up through the water jacket C above nozzle G, and 
out tube D. Mercury vapor from the boiler entering through 
tubes E flows through the nozzles F and G, is liquefied in the 
condensation chambers H and I, falls into the tubes K, and 
returns to the boiler through tube L. Gas from the vessel to 
be exhausted enters at M, flows past nozzle F, is compressed by 
the jet of mercury vapor in the condensation chamber H, and 
flows up through N to the intermediate pump. From here it 
flows past the nozzle G and is compressed through O into the 
chamber I to a pressure measured by the attached manometer, 
then out by tube P to the water aspirator." 

The speed of the pump as defined by Gaede's equation was 
observed to be about 250 ccm. per sec. 30 

General Remarks Regarding Exhaust Procedure 

As has been pointed out in a previous section, the vacuum 
actually attained by the use of any pump is dependent, first, on 
the type of pump used, and second, on the rate at which gases 
are given off from the walls of the vessel to be exhausted and 
metal parts inside it. In the case of the Gaede molecular pump, 
as stated previously, the degree of vacuum attainable (Pi) is de- 
pendent upon the exhaust pressure (P 2 ) produced by the rough 
pump. As the value of the ratio P 2 /Pi is about 50,000, it is 
evident that even with a rough pump pressure of one bar, the 
pressure attainable with this pump is less than 10~ 4 bar. In the 
case of the mercury vapor pumps there is theoretically no lower 
limit pressure, and the only limitation is therefore that due to 
the second cause mentioned above. 

The gases occluded on the walls of the glass vessels consist 
for the most part of water vapor and carbon dioxide gas along 
with slight amounts of carbon monoxide and other gases which 
are not condensible at the temperature of liquid air. Metal 
parts usually contain carbon monoxide and hydrogen gases.* 
In order to eliminate these gases it is essential to heat the glass 
walls and metal parts to as high a temperature as practicable. 

29 J. Washington Acad. Sciences 7, 477 (1917). 

3° M. Volmer, Ber. 52 (b). 804 (1919), has also constructed a similar form of two-stage 
condensation pump, which is described brief! v in an abstract in J. Chem. Soc. 116, ii, 225 
(1919). 

* See Chapter IV for discussion of the absorption of gases by glass and metals. 



72 



High Vacuum Pumps 




Fig. 29. Stimson's Form of Condensation Pump 



The longer the duration of the heating and the higher the 
temperature, the lower the pressure of residual gases. 

A usual procedure is to heat the glass vessels in an oven, 
during exhaust, for an hour or longer. For lead glass, the tem- 
perature in the oven should not exceed 360° C; in the case of 



High Vacuum Pumps 



73 



lime glass, the temperature may be raised to 400° C, and for 
vessels made of pyrex, the oven temperature may be increased to 
500° C. The oven may be heated either by gas flames, or more 
conveniently by electrically heated grids, as the latter method 
permits of a more uniform distribution of temperature inside the 
oven and also is more convenient for regulation. 




To Pump- 



Fig. 30. Vacuum Furnace for High Temperature Exhaust 



Where a very high degree of vacuum is desirable it is possible 
to heat the glass to temperatures higher than those mentioned 
above, by reducing the pressure of air in the oven itself, so that 
the glass walls will not collapse because of external pressure. 
For this purpose Langmuir devised the form of oven shown in 
Fig. 30. 31 

It consists of a metal chamber 7, which is open at the bottom 
but rests upon a base plate 8, with which it makes an air-tight 
joint. The chamber is provided with a heating coil wound on 

•>» I. Langmuir ,U. S. Pat. ,994,010 ,Ma: 30, 1911. 



74 High Vacuum Pumps 

the inside and separated from the walls by heat-insulating lining. 
The leads for this heating coil are shown at 11. Uprights 9 
are provided for the purpose of allowing the oven to be raised 
or lowered. As the chamber 7 is to be exhausted it is necessary 
to make the joint between it and the base plate 8 air-tight. 
This may be accomplished by means of a rubber gasket, and 
in order to prevent injury to this by the heat, the chamber 
and the base plate are cooled by water, which flows as indicated 
by the arrows through the tubes 23, 24, 25 and 27. Openings 
are provided in the base plate for the connection between the 
vessel to be exhausted and the pump, and also for exhausting 
the chamber itself. A rough pump is, of course, all that is nec- 
essary in the latter case. 

With this type of oven it is possible to heat the glass about 
100° C. higher than in an ordinary oven, so that the residual 
water vapor and other condensible gases are removed more 
completely. 

In the case of metal parts the elimination of gases is a more 
difficult matter. Where these parts are so constructed that 
current can be passed through them (wires or filaments) they 
ought to be heated to as high a temperature as the metal will 
stand without injury. In the case of hot cathode devices the 
anodes can be heated to incandescent temperatures by electronic 
bombardment. 32 Heating the metal parts in a vacuum furnace 
before putting them in the glass vessel also assists materially 
in the subsequent exhaust on the pump. Special care should 
be taken to remove all traces of grease and oil from machine- 
made parts, by washing in acetone and alcohol and drying 
thoroughly before assembling in the glass vessel. 

In order to eliminate mercury vapor and condensible gases 
emitted from the grease used on the ground glass joint between 
the pump and the vessel to be exhausted, it is necessary to 
interpose some form of refrigerating chamber in which these 
vapors are condensed, as shown at G in Fig. 23. (See also Appen- 
dix I.) 

The most efficient refrigerating agent is, of course, liquid 
air, which is now available in a large number of laboratories. 
Failing this, a suspension of solid carbon dioxide in acetone or 
ether may be used. In the latter case it is well to insert a tube 
containing P 2 5 between the oil pump and the fine pump to 
take care of water vapor. Observations in this laboratory have 
shown that in using a condensation pump it is possible to 

32 For illustrations of this the reader may refer to the following publications: 
I. Langmuir, Phys. Rev. 2, 450 (1913). 
S. Dushman, Phys. Rev. 4. 121 (1914). 



High Vacuum Pumps 75 

obtain practically as low pressures with solid C0 2 and P 2 5 
as with liquid air, but the interval of time required to attain 
this low pressure is ordinarily much longer with the former. 

The temperature produced by fresh liquid air evaporating 
freely into the atmosphere is about — 190° C. (83° K.), but rises to 
a higher value as the nitrogen boils away and leaves the oxygen 
behind. 33 With solid carbon dioxide a temperature of —78° C. is 
obtained. Table XIII shows the vapor pressures of a number of 
different gases at these low temperatures. In the case of methane, 
ethane and ethylene the pressures given have been extrapolated 
from the data given in the standard tables for higher tempera- 
tures, by plotting the value of log P against 1/T, where T is the 
absolute temperature. The values plotted in this manner are 
found to lie on a straight line, thus making the extrapolation an 
easy matter. 

Table XIV gives the vapor pressures of carbon dioxide, ice and 
mercury. In all cases the data for the lower temperatures have 
been extrapolated in the same manner as for those given in the 
previous table. 

As is evident from these data, ice and mercury have no appre- 
ciable vapor pressure at — 190° C, while carbon dioxide has a 
vapor pressure between 0.001 and 0.0001 bar at this temperature. 
Under these conditions any of the latter gas if condensed in the 
liquid air trap would produce a constant pressure of residual 
gas of at least 10 -4 bar. Under the same conditions ethylene 
and ethane would produce pressures that might exceed 10 bars. 
However, these gases are not met with in ordinary exhaust 
operations. The other gases are non-condensible at the temper- 
ature of liquid air, and are therefore removed by the pump. 

It is also evident that at the temperature of evaporating 
solid C0 2 ( — 78° C.) the vapor pressure of mercury is negligibly 
small, but that of ice is quite high, hence the necessity for 
using P 2 5 in order to take care of this. It is also advisable 
in all cases of exhaust operations not to use the refrigerating 
agent during the initial stages of heating, so that the bulk of 
condensible gases will be removed by the pump. Otherwise 
the vapors may be condensed in the trap and maintain a con- 
stant pressure of residual gases in the system for a very long 
time. 

Temperatures below — 190°C. may be obtained by working 
with liquid air under reduced pressure. As is evident from 
Table XIII, it is possible in this manner to obtain a temperature 

33 E. C. C. Baly, Phil. Mag. 49, 517 (1900). This paper gives complete data regarding 
the relation between composition and boiling point in the distillation of liquid air. 



76 



High Vacuum Pumps 



TABLE XIII 

VAPOR PRESSURE OF "NON-CONDENSIBLE" GASES, 
AT LOW TEMPERATURES 




Ethane (C 2 H 6 ) 



-150 


123 


7.6 


-180 


93 


.076 


-190 


83 


.0076 


-198 


75 


.00076 



High Vacuum Pumps 




Fig. 31. Arrangement of Exhaust System 



as low as — 200° C. At this temperature the vapor pressure of 
solid C0 2 is less than 10~ 5 bar, and it is therefore possible under 
these conditions to obtain extremely low pressures of residual 
gases. 



78 



High Vacuum Pumps 



.Either liquid air or solid C0 2 prevents the diffusion of vapors 
emitted by grease around the joint, as these vapors are all con- 
densible at these temperatures. 

Determinations in this laboratory of the vapor pressures 
of vacuum pump oils have shown that these range around 1 to 
0.1 bar at room temperature, decrease to about one-fifth this 
value at 0° C, and are negligibly small at —78° C. Stopcock 
grease and similar compounds possess even lower vapor 
pressures. 

Further details regarding the actual operation and care of 
typical exhaust systems are given in Appendix I. 



TABLE XIV 
VAPOR PRESSURE OF "CONDENSIBLE' 



GASES 



Temperature 
Degrees Centigrade 



Absolute 
Temperature 



Pressure 
in Bars 



Carbon Dioxide (CO2) 



-148 


125 


100 


-168 


105 


1 


-182 


91 


0.01 


-193 


80 


0.0001 



Ice (H 2 0) 34 



-20 


253 


1045 


-30 


243 


384 


-40 


233 


128 


-50 


223 


39 


-60 


213 


9.6 


-76 


197 


1.0 


-89 


184 


0.1 


-101 


172 


.01 


-111 


162 


.001 



Mercury (Hg) 



+30 


303 


3.7 


+20 


293 


1.6 (2.43) 


+ 10 


283 


0.65 (1.03) 





273 


.25 (0.47) 


-10 


263 


.087 


-20 


253 


.029 


-40 


233 


.0023 


-78 


195 


4.3 X 
10~« 


-180 


93 


2.3 X 

io-*« 



w Extrapolated from K. Scheele and W. Heuse's data, Ann. d. Phys. 29, 723 (1909). 

s& Extrapolated from Knudsen's data, Ann. d. Phys. 29, 179 (1909). However. C. F. Hill 
(Phys. Rev. 18, 113) has reeen ly obtained values which are considerably higher. These 
are given in brackets. 



High Vacuum Pumps 



79 



APPENDIX I 
Fig. 31 shows diagrammatically an arrangement of the Lang- 
muir condensation pump and accessory connections which is 
convenient for high vacuum exhaust operation. 




Fig. 32. 



Photograph of Set-up for Exhausting Coolidge 
X-ray Tubes 



An ionization gauge, G, or other tube to be exhausted, is 
connected through the liquid air trap T to the pump P. The 
rough side of the latter is connected to a McLeod gauge and also 
the oil pump. As mentioned, the tubing between the con- 
densation pump and the vessel to be exhausted should be as wide 
as possible. The oven for baking out during exhaust is indicated 



80 High Vacuum Pumps 

diagrammatically as 00. Fig. 32 is a photograph of a set-up 
such as is used in the exhausting of Coolidge X-ray tubes in the 
factory. 

Care of the Condensation Pump: According to the instruc- 
tions, 626 grams of absolutely clean mercury should be poured 
into the pump. Under normal conditions, with 300 watts input 
into the heater and a flow of 1000 cm. 3 per minute through the 
cooling coils, only the lower portion of the pumps should run 
warm. If for any reason the flow of water ceases and the grease 
around the joint is melted, the pump should be removed, the 
mercury emptied out, and the pump cleaned with gasolene as 
directed in the instructions. Very little mercury should con- 
dense in the glass grinding above the pump. If, however, 
the grinding rapidly becomes covered inside with mercury and 
feels warm, it is an indication that the pump is not exhausting 
and a cleaning is required. 

Some observations carried out in this laboratory on the vari- 
ation in exhaust pressure with energy input into the heater are 
of interest in this connection. The following table gives the 
watts used and the corresponding minimum pressure obtained 
as measured by an ionization type of gauge. The oil pump 
pressure was 0.0146 mm. of Hg. 



Watts in Heater 


Minimum Pressure in Bars 


130 


0.27 


150 


0.07 


170 


0.04 


180 


0.023 


200 


0.013 


220 


0.007 


240 


0.0025 


280 


0.002 


300 


0.002 



Care of Rubber Tubing: All rubber tubing for use in vacuum 
systems should be cleaned well inside before use. This is best 
accomplished by washing with a warm 10 per cent solution of 
caustic soda, then with water and alcohol, and finally drying 
thoroughly by blowing air through it, or exhausting with a 
rough pump. The rubber tubing between the condensation 
pump and glass tube leading to the mercury trap should be as 
short as possible. Heavy vaseline or grinding grease* should be 

* A good stopcock grease may be made by heating approximately equal parts of pure 
rubber and vaseline. The rubber should be cut into very fine pieces and the heating con- 
tinued until the mixture has about the consistency of heavy molasses. 



High Vacuum Pumps 81 

used to make the junctions air-tight, and after the tubing is in 
place a little castor oil should be dripped over the joints, and 
over the rubber tube itself. 

Mercury Trap: This is inserted next to the rough side of the 
condensation pump and is essential in order to prevent mercury 
from getting into the oil pumps, where it would gradually disin- 
tegrate the bearings. A very good scheme which has been used 
successfully in this laboratory is to make this trap quite large 
(about 1 liter volume) and fill it with broken pieces of glass 
tubing, thus increasing the surface for the condensation of 
any mercury vapor that diffuses out through the rough side 
opening of the condensation pump. 

Detection of Leaks: A small Tesla coil, one end of which is 
grounded, is a useful accessory device in all exhaust operations. 
The high tension terminal of the coil is encased in rubber tubing 
and provided with a wooden handle so that it can be touched to 
any part of the glass system. A pin-hole leak will show up by 
the direct passage of a spark to this point, while at all points 
there will be a uniform glow if the pressure is over a few bars 
and there will be no glow at all when the pressure is one bar or 
less. 

Seal-Off Procedure: Constrictions in glass vessels at points 
where they are to be sealed off after exhaust should not be too 
thick walled, otherwise a large body of glass will have to be 
heated during the seal-off, causing the liberation of a great deal of 
gas. Furthermore, the constriction should be torched till it is 
almost melting and the pump allowed to exhaust the gas thus 
liberated for about two minutes, after which the sealing off 
should be performed as rapidly as possible without heating the 
glass any more than absolutely necessary. 

The importance of these precautions may be judged from 
the following observations : An ionization gauge, having a vol- 
ume of about 100 cm. 3 , was exhausted till the residual gas pres- 
sure was less than 0.001 bar. On sealing this off without ob- 
serving the precautions mentioned, the pressure in the sealed off 
tube was 0.25 bar, whereas by torching the constriction first 
and sealing off afterwards, it was possible to obtain a residual 
gas pressure in the sealed off gauge of less than 0.01 bar. 



CHAPTER III 
MANOMETERS FOR LOW GAS PRESSURES 

For the measurement of pressures that lie between one at- 
mosphere and one cm. mercury, a standard form of mercury 
barometer is generally used. Such a method is obviously very 
insensitive when it is necessary to measure pressures below 
this range, and consequently a number of types of manometers 
have been developed by different investigators for this purpose. 

In the simplest type of low-pressure gauge, the difference 
between the actual pressure and that in an extremely good 
vacuum is measured by some very sensitive optical method. 
This is the principle of Rayleigh's manometer. On the other 
hand, the McLeod gauge represents an interesting application 
of Boyle's law to very low pressures. By compressing a given 
volume of the gas whose pressure is to be measured to a very 
small known volume, the pressure is amplified several thousand- 
fold and may be read directly. 

Again, instead of attempting to measure the pressure 
directly, use may be made of the fact that the amount of heat 
conducted from a surface varies with the gas pressure. 
Similarly, the damping effect of gas on a body set in vibration 
or rotation varies with the pressure. In each case, however, 
it is necessary to know the law of variation between the observed 
effect and the pressure. 

In the following chapter are described some of the different 
types of low-pressure gauges that have been used by different 
investigators. Only those forms are described in detail which 
have proved to be most generally useful in the present state of 
high- vacuum technique; while other forms, which are of more or 
less historical interest, are mentioned rather briefly. 

MERCURY MANOMETERS 
Rayleigh's Gauge 1 

The essential parts of this gauge (Fig. 33) are two glass 
bulbs, one of which communicates with a good vacuum by a 
tube C, and the other with the system in which the pressure 
is to be measured. Two glass pointers are sealed into the bulbs, 
and the latter are connected to a T-connection which forms the 
upper end of a barometric column A. Mercury can be raised 

» Phil. Trans. 196, A. 205 (1901) Zeits. physikal. Chem. S7, 713 (1901>. 



Manometers for Low Gas Pressures 



83 



and lowered in the bulbs by means of the reservoir D and the 
level thus brought up so as to be flush with the ends of the 
pointers. Any difference in pressure on the mercury in the two 
bulbs is then measured by gradually tilting the framework AK 
and observing the deflection on a mirror which is fastened 
vertically on top of the bulbs at /. According to Rayleigh this 
gauge can be used to read pressures between 1.5 mm. and 
1 X 10~ 3 mm. of mercury. 




Fig. 33. Rayleigh's Gauge 



A modified form of this gauge was used by K. Scheele and 
W. Heuse 2 for measuring the vapor pressure of water at tem- 
peratures below deg. C, and similar manometers have been 
constructed by M. Thiesen, 3 and E. Hering. 4 

More recently, an ingenious modification of Rayleigh's 
method has been used by C. F. Miindel 5 for measuring vapor 
pressures at very low temperatures. A very sensitive optical 
method for measuring slight differences in level of two mercury 
surfaces, developed by K. Prytz, 6 has been used extensively by 
different investigators in connection with Rayleigh's method. 7 

« Zeits. f. Instrk. 29, 344-349 (1909). K. Jellinek, Lehrbuch d. physikal. chem. I, 1, p. 
321. Ann. d. Phys. 29, 723 (1909). 

* Zeits. f. Instrk. 6, 89 (1886) and 24, 276 (1904). 

* Ann. d. Phys. (4), 21, 320 (1906). 

* Zeits. f. Physikal. Chem. 86, 435 (1913). 

* Ann. d. Phys. (4), 16, 735 (1905). 

' C. F. Miindel loc. cit., and M. Knudsen, Ann. d. Phys. (4) SS, 1435 (1910). 



84 



Manometers for Low Gas Pressures 



In the optical lever manometer, described recently by J. E. 
Shrader and H. M. Ryder, 8 the same object is attained by a 
very simple construction. The following description is quoted 
from the original paper: 

"A mercury U-tube manometer (Fig. 34) is formed in the 
usual manner, except that the surfaces of the mercury are so 
arranged as to be of relatively large area. Above one of the 
surfaces, within the tube, is arranged an optical lever as shown 



75 Pump 



lb source of 
gases or voporsi 




Fig. 34. Optical Lever Manometer 



in the illustration. This lever is supported by two knife edges, 
a-a, which rest on loops of wire, which in turn are sealed into the 
glass walls of the tube; a glass bead b, fused to the end of the 
lever arm, acts as a float on the mercury surface, and in this way 
transmits the motion of the mercury surface to the lever arm. 
A mirror M attached at the position shown acts in the usual 
manner to reflect a beam of light from a lamp to a scale, if the 
gauge is to be arranged as an indicating instrument. If the 
gauge is to be used for recording variations in pressure, the scale 
may be replaced by a photographic device such as is used in 
oscillographic work. 

* Phys. Rev. IS, 321 (1919). 



Manometers for Low Gas Pressures 



85 




Fig. 35. McLeod Gauge 



"The cross connection e provides an easy means of evacuat- 
ing the whole system with one pump located as shown. With 
this stopcock or mercury cutoff open, a zero reading can be 
easilv obtained, after which this connection may be closed and 



86 Manometers for Low Gas Pressures 

the gases or vapors introduced for measurement. This system 
provides also for the measurement of small variations in pres- 
sure, with an original pressure of any desired value, this value in 
no way affecting the absolute sensibility of the gauge." 

A sensitivity of 10~ 3 mm. of mercury is claimed for the 
gauge, and it certainly ought to prove useful in those cases 
where the McLeod gauge is inapplicable. 

McLeod Gauge 

The principle of this gauge consists in compressing a given 
volume V of the gas whose pressure P is to be measured, to 
a much smaller volume v and observing the resultant pressure 
p which in accordance with Boyle's law is given by the relation 

p = PV/v 

Thus the sensitivity of the gauge increases with increase in the 
ratio V /v. 

One of the simplest forms of McLeod gauge is shown in 
Fig. 35. The bulb V, to which is attached a capillary tube aa, 
is connected to the low-pressure system at E and also to the 
barometric column T. In order to avoid errors due to the effect 
of capillarity, a tube bb of the same diameter as aa is sealed on 
as a by-path to the larger tube E. To operate the gauge the 
reservoir B is raised, thus forcing the mercury in the barometric 
column upward until the gas in V is shut off from the remainder 
of the. system. 

As the mercury is raised further, the volume of gas V is 
compressed until finally the mercury in the capillary bb is level 
with the upper end of the capillary aa (corresponding to the 
point on the scale) . The pressure on the gas in the capillary 
is then evidently equal to that of the mercury column of height 
h. Now let a denote the volume of the capillary per unit length, 
and P denote the pressure in the system at E. Then it follows 
from Boyle's law that 

P = fr (41) 

Since a and V are constant for any particular gauge, it fol- 
lows that the pressure is proportional to the square of the 
observed value of h. It also follows from this equation that the 
smaller the ratio a IV the greater the sensitivity of the gauge. 
Practical considerations, however, make it impossible to use 
either extremely fine capillaries or very large volumes for V. 



Manometers for Low Gas Pressures 87 

The following data for a gauge used by the writer are of in- 
terest in this connection as an indication of the range of pres- 
sures that can ordinarily be measured with a McLeod gauge : 

Gauge No. 1 

7=171 cm. 3 , a = 0.00407 cm. 3 per cm. length (diameter of 

capillary = 0.72 mm.) . 

Hence, measuring h in cm., 

0407 h 2 
p = u.u*u/^ =2 ,38X10- 4 h 2 (mm. of mercury) 

= -^X2.38X10- 4 /* 2 = 0.317/* 2 (bar) 

That is, for k=l cm., P = 0.317 bar; and for h — 1 mm., 
P = 0.0032 bar, so that for a 10-cm. length of capillary aa, the 
range of pressures that could be measured with this gauge is 
from 0.003 to 32 bar. 

Actually, it is impracticable to make V larger than 500 
cm. 3 and with capillaries smaller than 0.5 mm. the mercury 
tends to stick badly and the gauge is very sluggish in operation. 
With 7 = 500, and a = 2X10" 3 (d = 0.5 mm.), 1 cm. on the 
capillary would correspond to 4X10 -5 mm. of mercury, or ap- 
proximately 0.053 bar, and 1 mm., to 0.00053 bar. In general, 
the lower limit of pressure that can be measured with a McLeod 
gauge is about 0.01 bar. 

It is evident that the McLeod gauge does not indicate the 
pressure of mercury vapor and condensible vapors such as those 
of oil, water, and ammonia. Even in the case of carbon dioxide 
the gauge is very inaccurate. In using it to measure very low 
pressures, such as those produced by a Gaede molecular or 
Langmuir condensation pump, a liquid air trap should be inserted 
between the gauge and the remainder of the system in order to 
prevent diffusion of mercury vapor into the vessel to be ex- 
hausted. 

Regarding the accuracy of the gauge for indicating the 
pressure of the so-called permanent gases (Hz, He, Ne, Ar, Oi, 
N2 and CO) a careful investigation carried out by Scheele and 
Heuse 9 has shown that if the bulb and tubing are carefully dried 
(to eliminate the presence of a film of water) the results ob- 
tained in the case of air are certainly reliable down to pressures 
of 0.01 mm. of mercury and are probably just as exact at lower 
pressures. 

» Ber. d. deutsch. Physikal. Ges. 10. 785 (1908). 



S8 Manometers for Low Gas Pressures 

Lord Rayleigh 10 found by means of his differential manom- 
eter that in the range of pressures 0.001 mm. to 1.5 mm. 
Boyle's law holds accurately for N 2 , Hi, and 2 ; and Scheele 
and Heuse 11 observed the same result with their membrane 
manometer. A very careful investigation on this point was 
carried out by W. Gaede 12 in connection with his work on the 
laws of flow of gases at low pressures. He found that in the 
case of nitrogen and hydrogen, when care is taken to dry the 
walls thoroughly, the McLeod gauge is quite accurate down to 
very low pressures (below 0.0001 mm.), while in the case of 
oxygen, errors are liable to arise because of the formation of an 
oxide scum on the surface of the mercury which causes the 
surface to wet the glass in the capillary. However, this scum 
may be removed by heating the capillary carefully and the 
mercury then becomes quite clean again. 

There are certain features about the McLeod gauge that 
must be carefully observed both in its construction and opera- 
tion. In sealing off the upper end of the capillary aa (Fig. 35), 
care should be taken to have the capillary bore terminate in as 
blunt a surface as possible, so as to ensure a fair degree of ac- 
curacy in reading the very lowest pressures. 

The rubber tubing connecting the reservoir B and the tube. 
T should be thoroughly cleaned and dried before use to get rid 
of any loose particles and also to eliminate as much as possible 
the injurious action of the sulphur present in the rubber. Only 
the cleanest mercury should be used and all glass parts of the 
gauge should be dried thoroughly before filling with mercury. 
A new McLeod gauge will be found to give very erratic results 
at the beginning until all the condensible vapors adhering to 
the walls have been removed by gentle heating with simultane- 
ous exhaustion. 

For extremely sensitive gauges, where the volume V is 
large, the mass of mercury to be raised and lowered is so great 
that the design shown in Fig. 35 becomes impracticable. In 
these cases, the reservoir T may be replaced by a wide bore 
glass tube with snugly fitting glass plunger. Where a rough 
vacuum line is available, the top of the reservoir can be closed 
by a rubber stopper through which passes a two-way stopcock ; 
one way being connected to the rough vacuum, and the other to 
the atmosphere. The mercury in T can then be raised or low- 

"• Phil. Trans. (A) 196, 205 (1901). 

" Ber. d. deutsch. Physikal. Ges. 11, 10 (1909). 

" Ann. d. Phys. 41, 289 (1913). 



Manometers for Low Gas Pressures 89 

ered by opening the stopcock to the atmosphere or to the rough 
vacuum respectively. 13 

In order to avoid the error which arises when reading the 
very small volume of the capillary at the upper end, it is often 
preferable to compress the gas in the capillary aa to a definite 
volume and then observe the height h of the mercury in the 
capillary bb above this level. Under these conditions, since 

it is evident that h is directly proportional to the pressure to be 
measured. The value of h may then be observed very accurately 
by means of a cathetometer. This method of using the 
McLeod gauge is, however, not as sensitive at low pressures as 
is the preceding method. Again, in some cases, where 
the range of pressures to be measured is fairly large, the 
single capillary aa may be replaced by two or more capil- 
laries of gradually increasing bore, the coarser bore being sealed 
onto the bulb V and the finer one on top of this. The serious 
objection to this construction, however, is the inaccuracy of the 
measurements at the junction between the two capillaries. 

While the construction shown in Fig. 35 is the usual form 
of McLeod gauge used in exhaust work, a number of modifi- 
cations have been suggested which are more convenient in 
special cases. An interesting construction is that designed by 
H. J. Reiff 14 and shown in Figs. 36 and 37. The advantages 
of this form are its compactness and avoidance of the use of 
rubber tubing which, as Reiff points out, sooner or later causes 
the mercury to get dirty. The gauge is mounted on a board 
which can be turned 90 deg. about the axis at C (Fig. 37). 
The system in which the pressure is to be measured is connected 
at R by rubber tubing. In the position shown in Fig. 36, the 
reservoir G and tube V 1 are filled with mercury up to the stop- 
cock H. To measure the pressure, the board is turned into a 
vertical position and H opened until the mercury rises in M 
to the desired level. The bulb G 1 prevents any mercury from 
overflowing into the tube V 2 . After the measurement is com- 
pleted the board is again turned into the position shown in Fig. 
36 and the mercury returned into the reservoir G. 

13 An excellent description of the construction of such a McLeod gauge, sensitive to 
pressures as low as 10 — 6 mm., is given by Gaede in the article referred to in footnote ( 12 ). 
He used a capillary tube 0.35 mm. in diameter, while the volume of the bulb was about 
1 liter. 

" Zeits. f. Instkunde, 34, 97 (1914). 



90 



Manometers for Low Gas Pressures 



In the same paper Reiff has also described a further modi- 
fication of this construction in which the readings are directly 
proportional to the pressure. Other forms of the McLeod gauge 
have been described by A. Wohl and M. S. Losantisch, 15 and 
L. Ubbeholde. 16 

MECHANICAL MANOMETERS 

A number of attempts have been made to construct low- 
pressure manometers indicating the mechanical deformation 
suffered by a surface under pressure. At ordinary pressures 




Fig. 36. Short Form of McLeod Gauge, Front View 



this principle has been utilized in the construction of the Bour- 
don Spiral. Ladenburg and Lehmann, 17 and subsequently M. G. 
Johnson and D. Mcintosh, 18 have described a low-pressure 
gauge consisting of a flat tapered glass tube bent in the form of 
a spiral. The walls are usually very thin, so that the device 
may be sensitive to small pressure differences. A glass mirror 
is attached to the end of the spiral and the latter is sealed 
into another chamber in which the pressure may be varied. The 
system whose pressure is to be measured is connected to the 

is Ber. d. deutsch. chem. Ges. 38, 4149 (1905). 

i« Zeits. f. angew. Chem. 19, 755 (1906). 

» 7 Verh. d. deutsch. Phys. Ges. 8, 20 (1906). 

»» J. Am. Chem. Soc. 31, 1138 (1909); Zeits. f. Physikal. Chem. 61. 457 (1908). 



Manometers for Low Gas Pressures 91 

spiral. In using the instrument, the pressure outside the spiral 
is varied until it is equal to that in the spiral, as indicated by 
the mirror, and the pressure outside is then measured by an 
ordinary mercury manometer. The device has been used for 
measuring the pressure of corrosive gases like chlorine and am- 
monium chloride vapor. A similar type of manometer has 



Fig. 37 Short Form of McLeod Gauge, Rear View 

also been used very recently by C. G. Jackson for measuring 
the dissociation pressure of cupric bromide. 19 These gauges are, 
however, not sensitive to pressures below about 100 bars. 

Scheele and Heuse's membrane manometer 20 consists of 
a very shallow cylindrical glass box separated into two compart- 
ments (parallel to the flat sides) by a thin copper membrane. 
One compartment is connected to the system, while the other 
is connected directly to a high- vacuum pump. The deformation 
of the membrane, due to the slight difference in pressure on 
the two sides, is then measured by noting the number of 
interference rings produced by the pressure of the membrane 
against a glass plate. 

» For further details regarding this type of manometer, refer to K. Jellinek. Lehrb. d. 
Physikal. Chem. I, 1, p. 638, also to the references given in footnotes ( l7 ) and ( l9 ). 
20 Zeits. f. Instrk. 29, 14 (1909). 

Ber. d. deutsch. Phys. Ges. 1909. p. 1. 



92 Manometers for Low Gas Pressures 

The instrument was found capable of measuring pressures 
down to about 0.0001 mm. of mercury, but difficulties were 
encountered in using it because of the continual gas evolution 
from the walls of the device. 

VISCOSITY MANOMETERS 

Theory 

In Chapter I it was shown that if a plane is moving in a 
given direction with velocity u relative to another plane situ- 
ated parallel to it at a distance d, there is exerted on the latter 
a dragging action whose magnitude is given bv the equation 

B-f " (8) 

where 77 denotes the coefficient ji viscosity, and B denotes the 
rate of transfer of momentum, per unit area. 

It was found, however, by Kundt and Warburg 21 that at 
very low pressures, where the mean free path of the molecules 
becomes of the same order of magnitude as the distance be- 
tween a moving and a stationary surface placed in the gas, 
there is distinct evidence of a slipping of gas molecules over 
the planes, so that the apparent viscosity is decreased. As the 
pressure is lowered the amount of this slip is found to increase 
and at very low pressures it varies inversely as the pressure. 22 

Denoting the coefficient of slip by 8, it can be shown that 
the amount of momentum transferred per unit area from the 
moving surface to that at rest is 

Thus, owing to slip, there is an apparent increase in the thick- 
ness of the gas layer between the two surfaces, which amounts 
to 8 for each surface. 

As has already been stated, Kundt and Warburg found 
that at very low pressures 8 is inversely proportional to the 
pressure, and approximately of the same order of magnitude 
as the mean free path L, of the gas molecules at the corre- 
sponding pressures. 

More generally, we can write 
8 = aL 
where a is a constant. It is evident that at very low pressures, 

« Pogg. Ann. 155, 340 (1875). 

22 "The diminution of the viscosity at very low pressures is well shown by an incandescent 
lamp with a broken filament. If this be shaken while the lamp is exhausted it will be a 
long time before the oscillations die away; if, however, air is admitted into the lamp, 
through a crack made with a file, the oscillations when started die away almost immedi- 
ately." Poynting and Thomson. Properties of Matter, pp. 218-220. 



Manometers for Low Gas Pressures 93 

where d is small compared to L, equation (42) reduces to 



Since* 1 = 0.35 ^J-^- 



»- u \oZ 



2X0.35. | M 

2ttRT 

That is, with a given gas at constant temperature, the rate 
of transference of momentum is directly proportional to the 
velocity of the moving surface and also to the pressure. It fol- 
lows from this that given the value of a, it would be possible 
from measurements on the mutual effect of a moving surface 
and one at rest, to measure the pressure of the gas. 

The exact interpretation of a from the kinetic theory point 
of view has, however, proved to be rather a difficult matter. 
While the further discussion of this subject must be deferred 
for a subsequent chapter, it may be observed that a relation of 
the same form as (43b) may also be deduced by considerations 
similar to those used by Knudsen in connection w r ith his investi- 
gations on the laws of molecular flow.f 

The relation deduced from this point of view is found to 
be slightly different from (43b) , but both methods of reasoning 
lead to an equation of the form 

B = kup ^^f (43C) 

where k is a constant, which may be slightly different for 
different gases and probably varies also with the nature of the 
surface. 

In applying the above considerations to the construction of 
a gauge, two different methods have been used. In the first of 
these, which we may designate for reference as the "decrement" 
type of gauges, a surface is set in oscillation and the rate 
of decrease of the amplitude of oscillation is taken as a measure 
of the pressure. Physically, the damping may be explained as 
due to the gradual equalization of energy between the moving 
surface and the molecules of gas striking it. 

In the second type of construction, a surface is set in 
continuous rotation and the amount of twist imparted to an 
adjacent surface is used to measure the pressure. The 
molecules striking the moving surface acquire a momentum 

*See Chapter I, equations (5), (7b) and (11). 
tSee Chapter I, page 31. 



94 Manometers for Low Gas Pressures 

in the direction of motion which they tend in turn to impart 
to the other surface. If the latter is suspended and free to turn 
about an axis which is perpendicular to the direction of motion 
of the rotating surface, it will be twisted around until the 
force due to the incident molecules is just balanced by the tor- 
sion of the suspension. We may, therefore, designate this as the 
''static" type of viscosity gauge, to emphasize the fact that 
observations with this method are taken under stationary con- 
ditions. 



Decrement Type of Viscosity Gauge 

A gauge based on this principle was first suggested by W. 
Sutherland 23 and subsequently a very careful investigation on 
the same subject was carried out by J. L. Hogg. 24 The con- 
struction used by the latter, which was essentially the same 
as that used by Maxwell and Kundt and Warburg in their 
determinations of the coefficient of viscosity is shown in Fig. 
38. A thin glass disc is suspended by means of a wire be- 
tween two fixed horizontal plates N. The wire carries a mirror 
which may be viewed through a plate glass window D by 
means of a telescope and scale. At the top, the wire is sup- 
ported by clamps and is connected to a soft iron armature 
J which is supported by the swivel head K. By turning this 
armature by means of an external magnet, the center disc can 
be set in oscillation and the rate of decrease of the amplitude 
of these oscillations is then observed by means of the telescope 
pointed at the window D. 

Now let T denote the period of oscillation, and Si and 5 2 
two successive amplitudes of oscillation. Solving the differen- 
tial equation for the rate of damping of the central disc, it can 
be shown that 

^=e 2 =€ x (44) 

O2 

where X is defined as the logarithmic decrement. That is, the 
amplitude of oscillation decreases in geometrical progression for 
successive equal intervals of time. The constant a depends 
upon the moment of inertia of the vibrating disc and its dimen- 
sions. 

Thus X is a measure of the rate of transference of momen- 
tum from the vibrating plate to the stationary plates. 

" Phil. Mag. 43, 83 (1897). 

m Proc. Am. Acad. 42. 115 (1906), and 46, 3 (1909). Contributions from the Jefferson 
Physical Lab., 1906, No. 4, and 1909. No. 4. 



Manometers for Low Gas Pressures 



95 




Fig. 38. Decrement Type of Gauge 

At higher pressures, since the viscosity is independent of 
pressure, the logarithmic decrement has a constant value which 
may be denoted by /. Denoting by /* the decrement due to 
the suspension itself, it was shown by Sutherland that the 
following relation ought to hold true : 



teH)" 



C 



(45a) 



00 



Manometers for Loiv Gas Pressures 



/TN 




U 



Fig. 39. Quartz Fibre Gauge 



where p is the pressure and C is a constant for the particular 
arrangement used. 

The results obtained by Hogg were found to be in satisfac- 
tory accord with this equation down to pressures of the order of 
0.0004 mm. of mercury in the case of hydrogen. 



Manometers for Low Gas Pressures 



97 



It is evident from the form of equation (45a) that the gauge 
is unsuitable for measuring very low pressures (say below 0.0001 
mm.) as the value of X then becomes comparable with that of 
fx, thus involving large experimental errors. Furthermore, as 
mentioned by Hogg, the construction of the gauge and its actual 
manipulation require extremely great care. 

A very recent contribution to the theory of this type of 
viscosity meter has also been published by P. E. Shaw. 26 He 
derives an equation of the form 

p = Ck (45b) 

and records measurements of pressures down to 0.35 X10 -3 
mm. of mercury. 

Quartz Fibre Gauge 

This method was originally suggested by I. Langmuir 26 
for measuring the residual gas pressure in a sealed off incan- 
descent lamp, and has been used in this laboratory in a number 




Fig. 40. Optical Arrangement for 
Quartz Fibre Gauge 



of investigations. It is specially useful in measuring low pres- 
sures of chemically active vapors such as those of chlorine, 
iodine, and mercury which are liable to attack metal parts. A 
discussion of the theory of the gauge and actual details as to 
its manipulation have been published by F. Haber and F. 
Kerschbaum. 27 

The construction of the gauge is shown in Fig. 39. It 
consists of a thin quartz fibre sealed into the top of a glass 

25 Proc. Phys. Soc. London, 29, 171 (1917). 
« J. Am. Chem. Soc. 35, 107 (1913). 
27 Zeits. f. Elektrochem, 20, 296 (1914). 



98 



Manometers for Low Gas Pressures 



tube. The fibre is set in oscillation by gently tapping the glass 
bulb and the rate of decrease of the amplitude of vibration is 
then observed by means of a telescope and lamp as shown in 
Fig. 40. 

Let t denote the interval of time required for the amplitude 
to decrease to half value. Then it has been shown by Haber 
that 

p\/~M=--a (46) 

where p denotes the pressure, M is the molecular weight of the 
gas, and a and b are constants for the particular quartz fibre. 
That is, for any gas, the pressure varies linearly with the recip- 
rocal of t. 

In the case where the gas to be measured is a mixture 
of different vapors, the sum of a number of terms p\/~M 
must be taken corresponding to the partial pressure of each 
constituent. 

The constant b in equation (46) is proportional to the 
diameter of the fibre, that is, the finer the fibre the smaller 
the pressure at which the amplitude will decay to half value 
in a given time. On the other hand, a is a function of the 
elastic properties of the fibre. 

It is evident from the form of equation (46) that b/a cor- 
responds to the value t at which the amplitude would decrease 
to half -value in a perfect vacuum. For calibration, it is nec- 
essary to obtain only two points, corresponding to the two 
constants a and b. One of these may be determined by observ- 
ing the value t Q in a very good vacuum, while the other 
point may be obtained by calibrating against a McLeod gauge 
with some gas of definite composition. 

The following data are given by Haber for a quartz fibre 
7.0 cm. long and 0.013 cm. in diameter. Air was used for 
calibration. 



Pressure 
in mm. Kg 


p\/M 


t (seconds) 


b 


0.00302 

0.00494 

0.00775 

0.0117 

0.01880 

0.0260 


0.01625 

0.02654 

0.0417 

0.0630 

0.101 

0.140 


74 
46 
31 
22 
12 
10 


1.22 
1.23 
1.30 
1.39 
1.23 
1.40 


a -0.0003 




Avg. 1.28 









Manometers for Low Gas Pressures 09 

Some measurements with air taken by Air. Huthsteiner in 
this laboratory, using a fibre 3.8 cm. long and 0.0045 cm. 
diameter, are given for comparison. 

Pressure in mm. Hg /(seconds) 



0.00058 105 

0.00342 31 

0.0080 16 

0.0190 6.5 



Plotting p against — gave a straight line whose equation is 

131 
103 p= — -0.655. For air, M = 28.96. Hence, for this partic- 



ular fibre, 



/ — 0.705 _ ^ oro 
p\/M=-~ 0.003o3 



Since / o = 200 in this case, it is evident that this fibre could not 
be used for measuring pressures below 0.0001 mm. of air. It 
also follows from the form of the above relation that the 
heavier the gas the lower the range of pressures over which the 
gauge may be used. 

The optical arrangement suggested by Haber (Fig. 40) may 
be varied in practice by fastening a scale to the back of the 
gauge and placing the lamp in such a position that the light 
beam passes practically parallel to this scale. The scale and 
tip of the quartz fibre are then sighted by means of a cathe- 
tometer. 

While Haber used tubes which were more or less flattened on 
two sides, ordinary cylindrically walled tubes are more con- 
venient and almost as satisfactory. As observed by Haber, 
care should be taken to tap the glass in such a manner that the 
fibre vibrates in the plane at right angles to the line of sight 
from the cathetometer. With a little experience, this can 
readily be accomplished. In view of the simplicity of con- 
struction and relative ease of manipulation, the quartz fibre 
gauge ought to find a useful field of application in low pressure 
technique, where the pressures to be measured are not below 
about 0.05 bar. 



100 



Manometers for Low Gas Pressures 




Fig. 41. Molecular Gauge 




Fig. 42. Rotating Commutator Connection 
for Molecular Gauge 



Manometers for Low Gas Pressures 101 

Static Types of Viscosity Gauge 

The molecular gauge suggested by I. Langmuir 28 represents 
a direct application of equation (43c). The construction and 
results obtained with a gauge built on this principle have been 
described by S. Dushman: 29 

"It consists of a glass bulb B (Fig. 41) in which are con- 
tained a rotating disc A and, suspended above it, another 
disc C. The disc A is made of thin aluminum and is attached 
to a steel or tungsten shaft H mounted on jewel bearings and 
carrying a magnetic needle NS. Where the gauge is to be used 
for measuring the pressure of corrosive gases like chlorine, the 
shaft and disc may be made of platinum. The disc C is of 
very thin mica, about 0.0025 cm. thick and 3 cm. in diameter. 
A .small mirror M, about 0.5 cm. square, is attached to the mica 
disc by a framework of thin aluminum. This framework carries 
a hook with square notch which fits into another hook similarly 
shaped, so that there is no tendency for one hook to turn on 
the other. The upper hook is attached to a quartz fibre about 
2 X 10~ 3 cm. diameter and 15 cm. long. 

"The lower disc can be rotated by means of a rotating 
magnetic field produced outside the bulb. This field is most 
conveniently obtained by a Gramme ring, GG, supplied at six 
points with current from a commutating device rotated by a 
motor (Fig. 42) . In this way the speed of the motor determines 
absolutely the speed of the disc, and the speed of the latter may 
thus be varied from a few revolutions per minute up to 10,000 
or more." 

By applying equation (43c) it can be shown that the angle 
of torque (a) on the upper disc is given by the equation 

2Vk)^\Rf (47) 

where t = natural period of oscillation of mica disc, 
k — moment of inertia of disc, 
r — radius of rotating disc, 
and co = angular velocity of rotating disc. 

Hence, for any one gauge, the torque on the upper disc is 
proportional to the product of the s peed o f rotation of the 
aluminum disc and the quantity p\/M/(RT). The sensitivity 
of the gauge can thus be increased by increasing the speed of 
rotation; also by illuminating the mirror and using a similar 

28 Phys. Rev. 1, 337 (1913). 

29 Phys. Rev. 6, 212 (1915). 



102 Manometers for Low Gas Pressures 

arrangement to that used for galvanometers, it is possible to use 
the gauge to measure pressures of the order 10 -3 to 10 -4 bar. 

The gauge actually used for measuring very low pressures 
showed a deflection of 1100 mm. per bar of air, at 1000 r.p.m., 
with the scale 50 cm. from the mirror. Up to a pressure at 
which the mean free path of the gas molecules becomes com- 
parable with the distance between the two discs, the deflections, 
at constant speed of rotation, were found to be proportional to 
the pressure as observed by a McLeod gauge. 

At extremely low pressures (below 5X10 -4 bar) the indica- 
tions of the gauge were found to be inaccurate because of two 
sources of error. Firstly, the rotation of the magnetic field pro- 
duced by the Gramme ring tends to induce eddy currents in the 
metal frame work used to hold the mirror ; and secondly, there is a 
tendency for the upper disc to start swinging especially at very 
high speeds of rotation of the aluminum disc. As the damping 
at low pressures is very feeble, it is very difficult to stop this 
oscillation when once started. 

Working independently of Langmuir, and about the same 
time, A. Timiriazefl 30 also suggested the application of equation 
(43c) to the construction of a low-pressure gauge. As he was 
primarily interested in determining the laws of slip for different 
gases his actual design is not suitable for a very sensitive gauge. 
Instead of using a rotating disc with a stationary disc situated 
symmetrically above it, Timiriazefl used a rotating cylinder 
with a stationary cylinder placed symmetrically inside it and 
suspended by a phosphor bronze wire. 

RADIOMETER GAUGES 
Crookes* Radiometer 

One of the first instruments to be used for detecting low 
gas pressures was the radiometer devised by Sir William 
Crookes in 1873. The instrument, which is described in all 
text-books, consists of a glass bulb in which a small vane or 
fly is mounted on a vertical axis. The vane has four arms of 
aluminum wire on which are attached four small plates of thin 
mica, coated on one side with lamp black. These plates are 
set so that their planes are parallel to the axis. If a source of 
light or heat is brought near the bulb, and the rarefaction is 
just right, the fly rotates, but at very low pressures the rotation 
practically ceases. 

Ann. d. Physik. 40, 971 (1913). 



Manometers for Low Gas Pressures 103 

The theory of the device was apparently not very well 
understood for a long time, and attempts to use it as a gauge 
for low pressures yielded very unsatisfactory results. Dewar 
has stated the case for this instrument as follows: 

1 ' The radiometer may be used as an efficient instrument of 
research for the detection of small gas pressures. For quanti- 
tative measurements the torsion balance or bifilar suspension 
must be employed." 31 

Some years ago Air. W. E. Ruder, of this laboratory, 
developed a method of using the radiometer for the measure- 
ment of the residual gas pressure in incandescent lamps. The 
following account was prepared by him at the request of the 
writer : 

''It was found that when exhausted to the degree required 
in an incandescent lamp the radiometer could not be made to 
revolve, even in the brightest sunlight. In order to get a 
measure of the vacuum, the radiometer vanes were revolved 
rapidly by shaking the lamp and the time required to come to a 
complete stop was therefore a measure of the resistance offered 
to the vanes by the gas, together with the frictional resistance 
of the bearings. The latter quantity was found to be so small 
in most cases that a direct comparison of the rates of decay of 
speed of the vanes gave a satisfactory measure of the degree of 
evacuation. In this manner a complete set of curves was 
obtained which showed the change in vacuum in an incandescent 
lamp during its whole life and under a variety of conditions of 
exhaust. The chief objections to this method of measuring 
vacua were the difficulty in calibrating the radiometer and the 
difference in frictional resistance offered by different radiom- 
eters. For comparative results, however, the method was entirely 
satisfactory." 

As a result of his investigations of the laws of heat transfer 
in gases at low pressures, Knudsen arrived at a clear explanation 
of the radiometer action and furthermore developed, along the 
same lines, an accurate gauge for the measurement of extremely 
low pressures. 

According to Knudsen, there is a mechanical force exerted 
between two surfaces maintained at different temperatures in a 
gas at low pressure. This is due to the fact that the molecules 
striking the hotter surface rebound with a higher average 
kinetic energy than those that strike the colder surface. In the 
case of the radiometer the blackened surfaces absorb heat from 



Proc. Royal Soc, A, 79, 529 (1907). 



104 



Manometers for Low Gas Pressures 



the source of light and the molecules rebounding from the vanes 
are therefore at a higher temperature than those striking the 
walls of the bulb. Consequently a momentum is imparted to 
the vanes which tends to make them rotate. 32 

Knudsen Gauge 

The principle of the gauge constructed by Knudsen 33 maj^ 
be explained by referring to Fig. 43. Let us consider two 
parallel strips A and B placed at a distance apart which is less 



=K 




Fig. 43. Elementary Diagram of Knudsen Gauge 



than the mean free path of the molecules. Let A be at the 
same temperature T as the residual gas, while B is maintained 
at a higher temperature TV On the side away from B, A will be 
bombarded by molecules having a mean velocity G, corre- 
sponding to the temperature T, as given by the equation 



4 



32 Two recent papers by G. D. West (Phys. Soc. London, 82, 166 and 222, 1920) deal 
rather fully with the theory of the radiometer, especially at medium pressures, and also 
with the forces acting on heated metal foil surfaces at low pressures. 

w Ann. Phys. 82, 809 (1910). 



Manometers for Low Gas Pressures 105 

These molecules will of course rebound from A with the same 
velocity. However, on the side towards B, A will be bombarded 
by molecules coming from B, and having a higher velocity G\ 
corresponding to the temperature T%. Consequently A will 
receive momentum at a greater rate on the side towards B, 
than on the opposite side, and will therefore be repelled from B. 
From theoretical considerations Knudsen has shown that 
the force of repulsion K per sq. cm. of the two parallel surfaces, 
when the distance between them is less than the mean free path, 
varies with the pressure and the temperatures T and 7i, ac- 
cording to the equation 



P Ti 

= 2\T~ 



K =2\f~ 1 (4<Sa) 

For small differences of temperature, and for the purpose 

of pressure measurements, this equation may be written in the 

form : 34 

T 

P = 4/(^ = dynes per sq. cm. (48b) 

1 1— 1 

In order to measure this force of repulsion, Knudsen uses 
the arrangement shown diagrammatically in Fig. 43. The 
strip A is replaced by a rectangular vane, cut out in the center 
and suspended by means of a fibre 5. Two strips BB which can 
be heated are placed symmetrically on opposite sides of this 
vane, and the force of repulsion is then balanced by the torsion 
of the fibre. By means of the mirror M, the deflection can then 
be measured in the same manner as in the case of galvanometers. 

For this arrangement, equation (48b) assumes the form: 

47r 2 7J9 T 
^~ At*ri ' T _ T dynes per sq. cm. (48°) 

where 

I = moment of inertia of the moving vane, 
r = mean radius of the moving vane, 
2 A =area of the vane A opposite each strip B, 
t = period of vibration of the vane, 
D = scale deflection, and 
d — scale distance. 
Since all these quantities can be measured directly, it 
follows that the device can be used as an absolute manometer, 
without the necessity of calibrating against any other gauge. 
It is also evident that the indications of this gauge must be 
independent of the gas to be measured. 

s * A simple derivation of this and the following equation has been given by G. W. Todd, 
Phil. Mag. 38, 381 (1919). 



106 



Manometers for Low Gas Pressures 



In his first paper on this subject, Knudsen mentioned several 
different forms of construction which may be used in making 
a gauge on the foregoing principle, but gives very few construc- 
tional details. One form which appears to be very simple in 
construction is that shown in Fig. 44. 



B B 



Fig. 44. Simple Construction of the Knudsen Gauge 



A A is a glass tube about 1.4 cm. diameter in which is 
sealed a narrow tube BB. The latter has a rectangular piece 
cut out at C, 0.41 cm. wide by 2.95 cm. in length. A piece of 
mica D is suspended in front of this opening by means of a 
fibre which is fastened at E. The tube A A can be heated by 
means of an external water-jacket FF. As the temperature of 
the water in the latter is raised, the mica plate is repelled by 
the "hot" molecules traveling through the opening C, and the 
amount of -deflection can be observed by means of a microscope. 

Variations of this construction are described by Knudsen 
in a later paper, 35 but very few details are given. E. V. Angerer 36 
has described a Knudsen manometer which consists of a silvered 
mica vane between two electrically heated platinum strips, 

35 Ann. Phys. 44, 525 (1914). 
»• Ann. Phys. 41, 1 (1913). 



Manometers for Low Gas Pressures 



10\ 



arranged as shown in Fig. 43. He states that pressures as low 
as 8X 10~ 7 mm. of mercury can be measured with it. 

The same type of design has also been used by J. W. Wood- 
row 37 on the one hand, and by J. E. Shrader and R. G. Sherwood 38 
on the other. 




Fig. 45. Woodrow's Modification of the Knudsen Gauge 



Woodrow's Modification of Knudsen Gauge 

The following description of Woodrow's form of Knudsen 
gauge is quoted from the original publication: 

' ' Several different gauges were constructed varying in sen- 
sitivity so as to be used at different pressures. A typical gauge 
is shown in Figs. 45 and 46 and the electrical circuits are given 

» Phys. Rev. 4. 491 (1914). 
39 Phys. Rev. 12, 70 (1918). 



108 Manometers for Low Gas Pressures 

in Fig. 47. The glass rods GG served as supports for the metallic 
parts of the gauge. All the internal electrical connections and 
adjustments, with the exception of the final leveling, were made 
before the outer glass walls 00 were sealed on at SS. The sus- 
pension W was a phosphor-bronze ribbon 50 mm. in length which 
had been obtained from W. G. Pye & Co. and was listed by 
them as No. 0000. The movable vane VV consisted of a rec- 
tangular frame of aluminum 0.076 mm. in thickness, the 




Fig. 46. Cross-sectional View Through the Middle 
of the Gauge Shown in Fig. 45 

dimensions of the outer rectangle being 30 by 36 mm. and the 
inner 26 by 30 mm. The heating plates PP were platinum strips 
4 mm. wide, 40 mm. long and 0.025 mm. thick. The deflections 
of the movable vane were obtained in the usual way by the re- 
flection of a beam of light from the mirror M. Fig. 46 is a 
cross-sectional view through the middle of Fig. 45. 

"All of the platinum connections were made by electric 
welding, as that was found much more satisfactory than the 
use of any kind of solder, especially when heated. After a little 
practice, it was possible to weld the thin platinum heating vanes 
to the heavy platinum wire so as to make a perfectly continuous 
contact throughout its width. The phosphor-bronze suspension 
was connected at both ends by threading through three small 
holes drilled into the flattened extremities of the platinum and 
aluminum wires respectively. The small loops DD were so 
placed that they supported the movable vane V except when 
the gauge was leveled for taking readings. This made the 
gauge readily portable and, by placing in the inverted position 
when connected to the molecular pump, the danger of the 
breaking of the suspension by vibration was eliminated. One 
gauge of medium sensitivity was constructed so as to be suffi- 
ciently steady to be used when connected directly to the molec- 
ular pump. Large glass tubing was employed in all the con- 
necting portions of the apparatus. 



Manometers for Low Gas Pressures 



109 



"A small electromagnet, shown at E in Fig. 45, was em- 
ployed in bringing the moving vane to rest. This was found 
to be quite necessary in working with the most sensitive gauges, 
since in a very good vacuum the damping is so small that 
the vane will not settle down sufficiently for the taking of 
readings for some time after an accidental disturbance has set 
it vibrating. It should be noted that the electromagnet must 
have either an air core or one of good, soft Norway iron, for 




Fig. 47. Electrical Connections of the Gauge Shown in Fig. 45 



otherwise the residual magnetism will produce a false zero if the 
aluminum vane is at all magnetic, as was the case with the 
samples of metal investigated in this laboratory. Under these 
conditions it is obvious that the electromagnet should be used 
only for damping and that the exciting current should be shut 
off while making observations. 

' ' Several methods were tried for determining the tempera- 
ture of the heating strips and that shown in diagram in Fig. 47 
was finally settled upon as giving the most satisfactory results. 4 
The potentiometer leads TT were connected by electric welding 
to the very extremities of the platinum heating vanes PP. 
The heating current was regulated by the variable resistance p 
and its value was read on the ammeter A. The resistance r 2 
was kept constant at 10,000 ohms and n varied to obtain a 
balance of the sensitive galvanometer G. The potentiometer 
battery C consisted of a carefully calibrated Weston Standard 
Cell. This arrangement gave an accurate method of measuring 
the resistance of the platinum strips PP, plus the heavy platinum 



110 Manometers for Loiv Gas Pressures 

wire ab, the total cold resistance being 0.17 ohm. This cold 
resistance was determined by plotting the curve connecting 
resistance and heating current under a constant low pressure 
and extrapolating backward to the intersection with the axis of 
resistance. If the resistance is measured for small currents, the 
value at zero current, that is the cold resistance, can be deter- 
mined very accurately. The temperature coefficient of resistance 
of the platinum, which contained a small amount of iridium, 
was carefully determined and was found to give a linear relation 
within the range of temperatures employed. The value of the 
coefficient was 2.35 XK)~ 3 ohms per deg. C. With this system 
one can determine the mean temperature of the heating strips 
with sufficient accuracy, the error for temperature difference of 
about 50 deg. C. being less than four per cent. " 

Woodrow also observes that in order to avoid electrical 
effects it 'was necessary to silver-coat the outside of the glass 
walls which were then grounded. Similarly the moving system 
was connected through the suspension to that terminal of the 
heating strips which was grounded. 

"With the gauge whose dimensions are given above, the 
period of a complete oscillation was 10 sec, and the calculated 
moment of inertia of the moving vane was 0.074 gm. cm. 2 This 
gives for the pressure, 

P = 2.9X10- 5 — ^;d (bars) 
, 1 1— 1 

T 

= 2.2X 10 -8 ~ ~d (mm. of mercury) 

1 1— 1 

where d is the deflection in mm. on a scale at a distance of one 
meter from the mirror." Thus with a temperature difference of 
100 deg. C, the gauge could be used to read pressures as low as 
3 X 10 -8 mm. of mercury. 

Shrader and Sherwood's Modification of Knudsen Gauge 

The construction used by Shrader and Sherwood differs in 
a few details from that used by Woodrow. In view of the 
importance of the Knudsen gauge for low pressure measure- 
ments, the description of this modification is worth quoting: 

"The gauge is shown in Fig. 48. It is enclosed in a hard 
glass tube two inches in diameter and nine inches long. The 
heating strip aa is of platinum, 0.018 mm. thick and 7.5 mm. 
wide with a total length of 18 cm. It is folded at the top form- 
ing a cross piece and two parallel sides. The ends are brazed 
to 20 mil tungsten leading-in wires at the bottom. Fifteen 



Manometers for Low Gas Pressures 



111 



mil tungsten wires b sealed into the glass-rod support serve as 
a spring support for the platinum strip. This allows accurate 
adjustment of the strip and sufficient tension is secured to keep 
the strip taut during heating. One of these wires is carried up 
the glass-rod support, sealed into it at c, leaving a free end d 




Fig. 48. 



Shrader and Sherwood's Modification 
of the Knudsen^Gauge 



to serve for electrical connection of the moving vane to the 
heating strip. Connection is made by the wire pressing under 
tension against the tungsten wire e to which the suspension of 
the vane is fastened. Potential leads of fine platinum wires Jf 
are welded to the strip about one centimeter from the ends and 
are brazed to tungsten sealing-in wires. 

"The movable rectangular vane g is made of aluminum 
0.0076 cm. thick. A standard size adopted is 3.2 cm. by 4 cm. 
outside dimensions, the width of the vane being 0.5 cm. Because 



112 Manometers for Low Gas Pressures 

of liability of warping during heat treatment the vane is stiffened 
by an aluminum wire passing through slits at the top and a hole 
at the bottom into which the wire is hooked and fastened firmly. 
For portability, two copper wires h are sealed into the glass-rod 
support while the free end formed loops around the rod, these 
forming guides for the vane. The mirror is fastened at the 
bottom of the vane by leaving a small projection of the aluminum 
at the lower edge and cutting out small tongues from the 
material of the vane on either side. The mirror is laid in place 
and the projection and the two tongues are pressed closely over 
it, holding it securely. 

" Silver mirrors were tried, but failed to withstand the heat 
treatment to which the gauge and system were subjected. 
Mirrors made by coating microscope cover glass with china 
decorators' platinum solution, followed by baking at 500 deg., 
solved this difficulty. 

"The distance between the heating strip and the vane is 
adjusted from outside the case by magnetic control on a piece 
of soft iron i sealed into a glass stem to which the suspension 
is fastened. 

"The suspension is 0.0005-inch tungsten wire. This is 
fastened to small aluminum hooks around which the wire is 
wrapped several times after which the hooks are pressed firmly 
together. This method is not difficult and holds the wire 
securely. A hook on the end of a tungsten wire sealed into a 
glass stem, the free end i passing through a capillary rod / on 
the glass support, serves to hold the suspension. * * * 

"A gauge such as has been described, using a 0.0005-inch 
tungsten suspension from 6 to 7 cm. long, has such a sensibility 
that a scale deflection of 1 mm. at a meter's distance with a 
temperature difference of 150 deg. C. between the heating strip 
and the movable vane indicates pressures of 1 X 10~ 8 to 5X 10~ 8 
mm. Hg. One gauge of other dimensions than those given above 
would indicate a pressure of 5X10 -9 mm. Hg. under the same 
conditions." 

The temperature of the heated strips is measured by sub- 
stantially the same electrical method as that used by Woodrow. 39 



39 L. F. Richardson (Phys. Soc. London, 31, 270, 1919) has described a form of Knudsen 
gauge in which he balances the force of repulsion by means of a magnetic field. The 
instrument seems, however, quite complicated in construction. 

A commercial form of Knudsen gauge brought out recently in Germany by H. Rieger 
is described briefly in Engineering, July 30, 1920. 



Manometers for Low Gas Pressures 



113 



RESISTANCE MANOMETERS 

At ordinary pressures the heat conductivity of gases, like 
the coefficient of viscosity, is independent of the pressure. 
However, as the pressure is decreased, a point is reached at 
which the heat conductivity begins to decrease with the pressure 
in a manner which is quite analogous to the phenomena ob- 
served in the case of viscosity measurements. Kundt and 
Warburg pointed out, as a result of their experiments on the 



/ 



w 



Fig. 49. Hale's Improved Form 
of Pirani Gauge 



coefficient of slip, that a similar phenomenon was to be expected 
in the case of heat conductance at low pressures. Subsequent 
experiments by Sutherland, Smoluchowski and Knudsen have 
shown that such is actually the case. 

These experiments have led to interesting speculations 
upon the mechanism of the heat transfer in gases between sur- 
faces which are separated by a distance which is comparable 
with or less than the mean free path of the molecules, and the 
more detailed discussion of this subject will be taken up in 
a subsequent chapter. 

The important experimental fact from the present point of 
view is that at very low pressures the observed coefficient of 



114 Manometers for Low Gas Pressures 

heat conductivity of gases varies with the pressure. E. Warburg. 
G. Leithauser, and E. johansen 40 applied this fact to the construc- 
tion of a gauge by measuring the change in resistance of a small 
bolometer strip; while W. Voege 41 used a small thermocouple 
attached to a wire heated by a constant alternating current. 
The temperature of the wire as observed by means of the 
thermocouple was found to be a function of the pressure. 

The fact that the heat conductivity cf gases at low pres- 
sures varies with the pressure has also been utilized by W. Rohn 
in the design of a vacuum thermo-element 42 which is exposed to 
a source radiating energy at a constant rate (an incandescent 
lamp maintained at constant voltage). In this case the thermo- 
element is enclosed in a glass bulb which is connected to the 
system in which the pressure is to be measured. At pressures 
above about 0.1 mm., the electromotive force is practically 
independent of the pressure, but as the pressure is decreased 
below this value, the heat less by conduction decreases, and 
the temperature of the thermo-element rises. Consequently 
the e.m.f. also increases. Between 0.1 mm. and 0.00 1 mm., 
the increase in e.m.f. varies approximately linearly with the 
logarithm of the pressure, but at still lower pressures the e.m.f. 
reaches a maximum value which remains constant as the 
vacuum is improved. 

Pirani-Hale Gauge 

M. Pirani pointed out that in order to construct a gauge based 
on the relation between the heat conducted from a wire and the 
pressure, three different schemes could be used. 

1. The voltage on the wire is maintained constant, and 
the change in current is observed as a function of the pressure. 

2. The resistance (and consequently the temperature) of 
the wire is maintained constant, and the energy input required 
for this is observed as a function of the pressure. 

3. The current is maintained constant, and the change in 
resistance observed as a function of the pressure. 

The first scheme was tried using an ordinary 110-volt 
tantalum-lamp. Better results were, however, obtained when 
the tantalum wire was clamped tightly to the anchor wires in 
order to keep constant the heat loss through the supports. With 
the improved instrument the two other methods were tried, 
using a Wheatstone bridge arrangement to measure the resist- 

*° Ann. d. Phys. 24, 25 (1907). 

41 Phys. Zeits. 7, 498 (1908). 

« Zeits. f. Elektrochem. 20, 539 (1914). 



Manometers for Low Gas Pressures 



115 



ance of the wire, and the third one finally recommended as the 
most sensitive for use in pressure measurements. 

While the principle of Pirani's gauge is thus extremely 
simple, the sensitiveness actually obtained by him was not very 
great, the lower limit of accuracy being around 0.1 bar. 

An improved form of this gauge was constructed by 
C. F. Hale, 43 which is shown diagrammatically in Fig. 49. The 
following description is quoted from Hale's paper: 

"A piece of pure platinum wire, 0.028 mm. in diameter and 
450 mm. long, is mounted upon a glass stem carrying two radial 
glass supports near the top and three at the bottom. The wire 



Mttflorntttr 




Fig. 50. A Diagram of the Electrical Connections of the Gauge Shown in Fig. 49 



is anchored to these radial supports by means of short pieces of 
platinum wire 0.052 mm. in diameter. The anchor is fused 
into the radial supports at one end, and the other end is made 
fast to the manometer wire either by an arc weld or by a tiny 
glass bead. The leading-in wires at L, to which the ends of 
the manometer wire are welded, are of platinum, 0.31 mm. in 
diameter. All of the platinum wire employed in making the 
manometer was drawn from the same lot of larger wire and was 
assumed to be of uniform purity. The temperature coefficient 
of the manometer wire was found to be 0.00376 per cent per 
degree. The platinum leading-in wires are joined to heavy cop- 
per leads (1.1 mm. diameter) by welded joints, and these joints 
are fused into the stem as in electric lamps. The stem is sealed 

« Trans. Am. Electrochem. Soc. 20, 243 (1911). 



116 Manometers for Low Gas Pressures 

into a tubular bulb 3.2 cm. in diameter and 11.4 cm. long. 
This size of bulb is easily obtained, since it is the size regu- 
larly used for 50-watt tubular lamps, such as are commonly 
employed for galvanometer illumination. At 5 is a tube by 
which the manometer is connected with the system whose pres- 
sure is being studied. The upper end of the stem T is consid- 
erably elongated to permit the complete immersion of the 
manometer in a constant temperature bath, whose temperature 
was approximately zero deg. C. This stem tube is made of 
sufficient length to leave 15 cm. of it above the level of the bath, 
a provision which we found to be necessary in order to avoid 
the condensation of atmospheric moisture upon the top of the 
tube and the leading-in wires during humid weather. For 
electrical insulation this tube is packed with purified dry asbes- 
tos wool." 

A diagram of the electrical connections is shown in Fig. 50. 
A Wheatstone bridge arrangement was used for measuring the 
resistance changes; and in order to increase the sensitivity 
of the gauge, an exact duplicate was exhausted as carefully as 
possible to an extremely low pressure, sealed off, and inserted 
in one arm of the bridge as a compensator. Both the com- 
pensator and manometer were kept immersed in the constant 
temperature bath. Ri was a manganin wire resistance of 925.6 
ohms, and R 2 a decade plug box containing 10,000 ohms. The 
strength of the current, as indicated by the milliammeter Am, 
was maintained constant at 9.25 X10~ 3 amp. by means of the 
battery and resistance R3. This current was sufficient to raise 
the temperature of the wire in the manometer and compen- 
sator to about 125 deg. at the lowest pressures. 

In calibrating the gauge against a McLeod gauge care had 
to be taken to keep mercury vapor out by means of a liquid- 
air trap inserted between the manometer and the remainder 
of the system. Fig. 51 shows calibration curves obtained with 
air and hydrogen at different pressures. 

The difference is due to the higher conductivity of hydro- 
gen, so that the indications of the manometer are dependent to 
a certain extent upon the nature of the gas used. Hale's meas- 
urements show that the lower limit of sensitivity for a gauge 
of this construction is about 0.00001 mm. (i.e., 0.0133 bar). 

More recently some further measurements with a Hale 
gauge have been carried out by Misamichi So. 44 and N. R. 
Campbell. 45 

" Proc. Physico-Mathem. Soc. Japan, 3rd. Ser., 1 , 152 (1919). 
*s Proc. Phys. Soc. S3, 287 (1921). 



Manometers for Low Gas Pressures 



// 



The construction of gauge used by the former differs in a 
few slight details from that of Hale. It was found that the sen- 
sitivity of the gauge is higher the lower the temperature of 
the surrounding bath. At zero deg. C, and using a heating 




V * 77 7T'7f^~i 



h u sr h i-j h tj 

Ktiistante. 



t' h /' /* f-r/'f/ h // /<><> '" '"~ 



Fig. 51. Calibration Curves of the Gauge Shown in Fig. 49 

current of 0.03 amp. for a platinum wire 0.076 mm. in diameter, 

the sensitivity as measured by j- . -^ was observed to be 

1 .38 X 10~ 3 per 1 X 10~ 4 mm. of mercury. Furthermore, varying 
the heating current from 0.03 to 0.05 amp. was found to produce 
no change in sensitivity. 

Instead of measuring the change in resistance, Campbell 
measures the potential which must be supplied to the Wheat- 
stone bridge to keep the resistance (and therefore the tempera- 
ture) of the wire constant. Three manginin resistances are 
chosen so that the bridge is balanced when the manometric wire 
is at a convenient temperature, say 100 deg. C. A voltmeter 
is connected to the terminals of the bridge, and the potential 
across the whole bridge varied by means of a rheostat in the 
batterv circuit, until a balance is obtained. 

If' I r is the potential required for a balance when p = o, and 
V is the potential at any pressure, p, it is found that 



V*-V 



- = k.'f(p) 



(49) 



118 



Manometers for Low Gas Pressures 



where k is a constant for any given gauge and / (p) is a function 
of the pressure. The function is actually found to be approxi- 
mately proportional to p. For pressures ranging as high as 
0.15 mm., as pointed out by Campbell, this method of using the 
Pirani gauge is specially adapted where it is desirable to meas- 
ure pressures greater than 1 bar. For such pressures the method 
used by Hale does not give a linear relation between change in 
resistance and pressure. 

A hot-wire manometer based on the same principle has also 
been described bv T. Tschudv. 46 



IONIZATION GAUGES 

An electron stream passing through a gas will ionize the 
latter when the velocity of the electrons exceeds a certain min- 
imum value. In this process, an electron is knocked out of 
the neutral atom by the incident electron, with the result that 
the residual portion of the atom is positively charged. The 
relation between the velocity u of the electrons and the voltage 
V required to produce this velocity is given by the equation : 

Y 2 mu 2 = Ve (50) 

where 

e = charge on electron 
m = mass of electron. 
During recent years the ionizing potentials of a large number 
of gases and vapors have been determined with a high degree of 
accuracy and have been found to vary from. 4 to 5 volts for the 
alkali metals to 25 volts for helium. 

The amount of ionization produced by a given electron cur- 
rent increases with the pressure and while this fact has been used 
as a qualitative guide for the detection of low gas pressures, 
it is only recently that attempts have been made to apply this 
principle to the construction of an actual measuring device. 

O. E. Buckley 47 has published a short paper on the results 
obtained with a manometer of this type in which no details 
are given as to the actual construction. The gauge consists of 
three electrodes which are used as cathode (source of electrons) , 
anode, and collector of positive ions respectively. As source of 
electrons a Wehnelt cathode or incandescent tungsten filament 
is used. The collector electrode is placed between the anode 
and cathode, and connected through a galvanometer to the 
negative terminal of a battery whose positive terminal is eon- 
is Elekt. Zeits. 39, 235 (1918); Electrical World, 75, 137 (1919). 
47 Proc. Nat. Acad. Sciences, 2, 683 (1916). 






Manometers for Lou Gas Pressures 



119 



nected to the most negative end of the cathode. The anode 
potentials used range from 100 to 250 volts, while the magni- 
tude of the electron current is varied from 0.2 to 2.0 milli- 
amperes. At a pressure of 10 -3 mm. the ionization current was 
observed to be about one- thousandth that of the electron cur- 
rent and proportionately less at lower pressures; so that with 



TO Y/tCVl/f-l 



niLi / a finer ck 




gai vAKorrerer/r 



Fig. 52. Ionization Gauge and Connections 



an electron current of 2.0 milliamperes, pressure below 10~ 6 mm. 
could be measured quite easily. 

According to Buckley "the exact forms of the electrode are 
not of great importance." However, subsequent experiments 
by C. G. Found and S. Dushman 48 showed that certain designs 
are much better than others. A gauge consisting of three hair- 
pin filaments placed in parallel planes shows erratic effects at 
low pressures because of charges on the walls. Of the many 
types of construction tested, that shown in Fig. 52 was found 
to have the best characteristics for measuring low pressures. 
This illustration also shows the method of connecting up the 
electrodes. 

48 Phys. Rev. 17, 7 (1921) 



120 Manometers for Low Gas Pressures 

The gauge consists of two tungsten filaments, each wound 
in the form of a double spiral and mounted co-axially on a 
four-lead stem which is sealed into the upper end of a glass 
tube about 4 cm. in diameter and 12 cm. long. The inner 
spiral is made of 5 turns of 0.125-mm. tungsten wire wound on 
a 2.25-mm. mandrel. The outer spiral is made of three turns 
of 0.125-mm. tungsten wire wound on a 3.65-mm. mandrel. 
Surrounding the spirals is a molybdenum cylinder about 12 
mm. in diameter and 12 mm. long which is supported on a two- 
lead stem at the lower end of the tube. 

Before using the gauge for any measurements, it is of course 
absolutely essential that gases occluded in all metal parts and 
water vapor on the walls should be thoroughly eliminated.* 

The best conditions for the operation of the gauge were 
found to be as follows : 

(a) For very low pressures {below 1 bar): 250 volts on the 
anode, — 20 volts on the collector cylinder, and a maximum 
electron current of 20 milliamperes. Under these conditions, 
1X10 -6 amp. positive ionization current corresponds to 0.0132 
bar argon. 

(b) For higher pressures (1 to 50 bars): 125 volts on the 
anode, — 20 volts on the collector cylinder, and an electron 
current of 0.5 milliampere. In this case, 1X10 -6 amp. ioniza- 
tion current corresponds to 0.5 bar argon approximately. 

Fig. 53 shows characteristic curves at different electron 
currents. The greater the electron current used, the lower the 
upper limit of pressure at which the linear relation is still valid. 

It will be observed from these curves that at constant 
pressure the ionization current is not quite proportional to the 
electron current. For measuring a considerable range of pres- 
sures it is desirable to have this proportionality, since it is then 
possible to increase the electron current as the pressure is 
lowered and thus increase the sensitivity of the gauge. The 
following method of connection has been found to give a linear 
relationship between ionization and electron current and may 
therefore be used instead of the arrangement just described. 
The inner filament is used as collector, the outer filament as 
cathode and the cylinder as anode. With this connection the 
ionization current is practically independent of the anode volt- 
age between 125 and 250 volts. The sensitivity is not quite as 
good as with the first method of connection, 1 X 10~ 6 amp. 
positive ionization corresponding to about 0.032 bar argon. 

* See Chapter II, pp. 71 -7.1. 



Manometers for Low Gas Pressi 



121 



An interesting result which was found on studying the 
behavior of the gauge with different gases is that at constant 
pressure and with the same conditions as to anode voltage and 
electron current, the ionization current increases with the 
number of electrons in the molecule. Thus the number of 
electrons in an argon molecule (or atom) is 18, while in a mer- 
cury molecule (which is also monatomic) the number of elec- 
trons is 80. The ionization currents at constant pressure are 



40o 

3e>o 


—\ 


1 1 1 


1 1 1 1 1 » 1 I 


I I r i r-r 


i l r 


r r- 


3ZO 












/ - 


Z80 












- 


24c 












- 


ZOO 












- 


/(,0 












- 


/ZO 






/y^ 






~ 


BO 
+o 




& 


s <t^--** — 


cuf&^ 




- 






•""T""*l 1 


1 1 1 1 1 1 1 1 


1 1 1 1 1 1 


.1 I I 


i I 



0/ O.Z 03 O.V QS a.6 0.7 OS 0.9 Ao /•/ /.Z 
Fig. 53. Characteristic Curves of the Ionization Gauge 

found to be in approximately this ratio. Experiments with 
iodine and water vapor showed that the ionization currents in 
these cases, as compared with that for argon at the same pres- 
sure (and same electron current) correspond to electronic num- 
bers of 106 and 10 respectively, if that for argon is taken at 
18. . This generalization is apparently not quite true for hydro- 
gen and helium. The ionization currents in these cases corre- 
spond to much larger atomic numbers. For all ordinary cases, 
however, the calibration for nitrogen (14 electrons per mole- 
cule) may be used as a general guide to the value of the 
pressure. 

The ionization gauge, as just described, has been found to 
be very useful in investigating the pressure changes in incandes- 
cent lamps and hot-cathode devices after sealing off from the 
pump. The ease of construction and simplicity of manipula- 
tion ought to make it a very useful device in high-vacuum 
technique. Instead of a tungsten filament as emitter of electrons, 
a Wehnelt cathode may be used. This consists of a platinum 



122 Manometers $ or Low Gas Pressures 

wire coated with oxides of the alkaline earth metals and its 
construction and characteristics have been described by H. D. 
Arnold. 49 This type of cathode has the advantage over one of 
tungsten for factory use because it is not apt to be destroyed 
by accidental leakage of air into the gauge while the filament is 
lighted. 

Some results with a three-filament ionization gauge have 
also been published by Misamichi So. 50 The ionization currents 
were, however, measured at constant cathode temperature, and 
since the electron emission is affected by gas pressure no linear 
relation was observed between pressure and ionization current. 



* Phys. Rev. 16, 70 (1920). 

*° Phys. Math. Sec. Jap. Proc. I. p. 76 (1919). 



/ 28 

CHAPTER IV 

SORPTION* OF GASES AT LOW PRESSURES 

While the use of vacuum pumps is undoubtedly the most 
generally applicable method of obtaining very low pressures, 
there are other methods of a physical chemical nature which 
are of great utility and importance in high vacuum technique. 
Charcoal, palladium black, and similar substances have been 
found to absorb large volumes of gas when exposed to very low 
temperatures. The high reactivity of alkali and alkaline earth 
metals with all gases except argon, helium (and the other ele- 
ments of the inert group) has been utilized by different investi- 
gators for "cleaning up" residual gases. The fact that the 
electrical discharge in a low pressure tube causes a gradual dis- 
appearance of the gas has been known for a long time and ex- 
plains the progressive "hardening" of the gas-filled X-ray tubes. 
In the incandescent lamp industry various chemicals or "getters " 
are also used for the purpose of improving the vacuum in the 
lamp after it is sealed off from the pump. All these are illustra- 
tions of physical chemical methods of producing high vacua, 
which we shall discuss in this and the following chapter. 

(I) ADSORPTION OF GASES ON CHARCOAL 1 
Dewar's Investigations on the Use of Charcoal in the Production of 

High Vacua 

That charcoal and other substances in a finely divided state 
have the power of taking up large volumes of different gases 
was observed even in the 18th century. Sir James Dewar 2 was 
the first investigator to make use of this phenomenon for the 
production of high vacua. He observed that charcoal made 
from coconuts has very much higher adsorptive power than that 
from other sources. He also found that by heating the charcoal 
in vacuo for a long time, to expel gases already adsorbed, and 
then cooling it to a low temperature, large volumes of the 
ordinary gases could be readily "cleaned-up," so that the pres- 
sure in a sealed-off bulb was diminished to a very low value. 
Thus, in the case of a 2000 cm. 3 bulb containing air at 2. 19 mm. 

* See page 125 for definition of this term. 

1 The literature on this subject is so immense that it is impossible to do more than refer 
briefly to the most important results. For further references the reader may consult the 
following: 

W. Ostwald. Lehrb. d. allgem. Chem., I, Aufl. 1, p. 778 (Reference to literature previous 

to 1890). 
H. Preundlirh. Kapillarchemie (1909) pp. 91-125. 
> Proc. Roy. Soc: 74, 122 and 127 (1904); Encycl. Britan. Vol. 16, p. 751 (1912); Engi- 
neering (London), June 15, 1906; ib., June 14, 1917. His first investigations were reported 
in Mature, July 15, 1875. 



121+ 



Sorption of Gases at Low Pressures 



pressure, 20 grammes of charcoal cooled in liquid air ( — 185 
deg. C.) effected a reduction in the pressure to 0.00025 mm. 
The adsorptive power for different gases was observed, in general, 
to increase with the boiling point of the gas. Some of the earlier 
observations are shown in Table XV, although it must be noted 
that much larger adsorptions have since been obtained owing 
to improved technique in the preparation of the charcoal. The 
volumes adsorbed are given in cm. 3 at deg. C. and 760 mm. 
pressures. 

TABLE XV 
GAS ADSORPTION ON CHARCOAL (per cm') 








Boiling 

Point 

Deg. Cent. 


Volume 
Absorbed 
at 0° C. 


Volume 
Absorbed 
at-185°C. 


Helium 

Hydrogen 

Argon 

Nitrogen 

Oxygen 


—268.6 
—252.9 
—186.2 
— 195.8 
—183.0 


2 cm 3 

A 

15 

18 


15 cm 3 
135 
175 
155 
230 



The effect of temperature on the relative adsorption of 
helium and hydrogen is shown in Table XVI. "It will be 
observed that the adsorption of helium, small in comparison to 
that of other gases, even hydrogen, increases therefore enor- 
mously at the lowest temperature," which is below the boiling 
point of liquid hydrogen. 

Further experiments on the use of charcoal for the pro- 
duction of high vacua were carried out by Blythswood and 
Allen. 3 Their results are extremely interesting. They observed 
that by using charcoal at the temperature of liquid air, very 
large volumes of air .could be adsorbed. The rate of adsorption 
was found to be given accurately by the first order reaction 
equation. 

dx 



dt 



= k (A-x) 



where 



and 



x = amount adsorbed at time t 
A = total amount adsorbed when equilibrium is attained, 

k = constant. 



•Phil. Mag. 10, 497 (1905) 



.Sorption of Gases at Low Pressures 



125 



In one experiment, using 216 gms. charcoal, a volume of 
about 925 cm. 3 was exhausted from an initial pressure of 40 mm. 
to 0.0009 mm. of mercury in about 3 hours. 

Absorption, Adsorption, Occlusion, and Sorption 

The clean-up of gases by charcoal and similar substances 
is apparently a complex phenomenon. It is certainly not a case 
of chemical reaction in the same sense as the clean-up of oxygen 
by a heated tungsten filament (where W0 3 is formed as a result 
of the reaction), although there is some question as to whether 
in the case of oxygen taken up by charcoal there is a chemical 
action. Also we are familiar with the occlusion of gases by 
metals. Here we are apparently dealing with true cases of 

TABLE XVI 

RELATIVE ADSORPTION OF HYDROGEN AND HELIUM AT 

LOW TEMPERATURES 



Temp. 
Deg. Cent. 


Helium 

2.5 

5. 
160 
195 


Hydrogen 


—185 
—210 
-252 
-258 


137 
180 
250 



solution, obeying laws similar to the solutions of nitrogen or 
oxygen in water. While there is some evidence of similar phe- 
nomena in the specific case of charcoal and hydrogen (see later) 
a theory of solution will not account for the general phenomena 
of clean-up of gases by charcoal. On the other hand, we find 
that all clean surfaces, after evacuation, absorb definite amounts 
of different gases. This seems to be a case of condensation on 
the surface, of a layer of gas about one atom in thickness. The 
gas molecules are attached to the surface by quasi-chemical 
forces. Increase in temperature causes rapid evaporation, while 
decrease in temperature leads to equally rapid condensation of 
gas on the surface. To distinguish these different kinds of 
physical chemical reactions, certain terms have been introduced 
into the literature on the subject. 

J. W. McBain 4 has suggested the term "sorption" as a 
"generic and non-hypothetical term for phenomena which fre- 
quently occur together," to include all cases of clean-up of gases 
by metals, charcoal, or other substances. 

< Phil. Mag. (6). 18, 916 (1909). 
Zeits. physikal. Chem. 68, 471 (1909). 



126 Sorption of Gases at Low Pressures 

The surface condensation of gases is usually referred to as 
adsorption, while the solution of gases in metals or liquids is 
regarded as an absorption phenomenon. The term "occlusion" 
is also used frequently in referring to the gases present in metals. 
No doubt, a large number of cases of occlusion of gases by metals 
ought to be classified as true absorption (solution) phenomena; 
while other cases must be regarded as illustrations of adsorption 
reactions. Under these conditions the use of the term occlusion 
seems superfluous. While the theories of sorption phenomena 
are discussed in a subsequent section, it has been considered best 
to introduce these terms in the present connection because of 
their value in the classification of the different cases of clean-up. 

Adsorption of Gases on Charcoal. General Investigations 

The clean-up of gases by charcoal is to a great extent an 
adsorption phenomenon, the condensation of the gas occurring 
on the large surface presented by the pores in the charcoal. 
The adsorptive power varies widely with the method of prepara- 
tion and structure, so that it is impossible to draw any conclusions 
by comparing the results obtained by different investigators. 
On the other hand, it has been possible to obtain interesting 
results by studying the behavior of any given specimen of char- 
coal, and from these results have been derived certain general 
conclusions regarding the "laws" of adsorption phenomena. 

The relation between the amount of gas adsorbed at con- 
stant temperature and the residual pressure is of great impor- 
tance. The measurements are carried out as follows : The char- 
coal (or other solid adsorbent) in a tube is heated to a high tem- 
perature (400 deg.-600 deg. C.) and simultaneously evacuated 
from previously adsorbed gases. A measured volume of gas is 
then brought in contact with this material and the pressure of 
the residual gas measured after eouilibrium is attained. This 
operation is repeated until, finally, the adsorbent becomes 
saturated. 5 

Most of the investigators in this field have measured the 
adsorption at pressures above 1 mm. of mercury, and there are 
very few published data on the adsorptive power of charcoal at 
the low pressures which are of interest in vacuum technique. 

5 Illustrations of the i pparatus used and method of measurement are given in the 
following: 

J. Dewar, Encycl. Brit. 16, 751 (1912) Fig. 5. 

M. W. Travers, Proc. Roy. Soc. 78, 9 (1907). 

I. F. Homfray, Zeits. physikal. Chem. 74, 129 (1910). 

A. Titoff, Zeits. physikal. Chem. 74, 641 (1910). 

J. B. Firth, Zeits. physikal. Chem. 86, 294 (1913). 



Sorption of Gases at Low Pressures 



127 



H. Baerwald 6 showed that by heating charcoal to over 500 
deg. C, its adsorptive power is increased considerably; also that 
charcoal from coconut shell is a much better adsorbent than that 
from the soft part of the nut, or from wood. 

The adsorption of nitrogen, oxygen, and air on coconut 
shell charcoal at about 18 deg. C. has been measured by F. 
Bergter. 7 




JO £0 30 40 50 €0 70 SO 90 
Vo/urne per* GH. 




Fig. 54. 



jo 15 eo 
fo/ume pen GM. 

Adsorption ox* Gases on Charcoal at 
Low Pressures (Claude) 



The measurements at low pressures (1-10 mm. mercury) 
show that at the same pressure oxygen is adsorbed in about 30 
or 40 times as great an amount as nitrogen, while the adsorbing 
power of air is about 3 times that of nitrogen. At low pressures 
the amount adsorbed is proportional to the final pressure. It 
was also observed that in the case of nitrogen, about 96 per cent 
of the total amount is adsorbed almost instantaneously, while 
the rest is adsorbed very slowly. 

In the following tables and curves of results obtained by 
different investigators, the pressure is given in mm. of mercury. 
the volume adsorbed, in cm. 3 (measured at deg. C. and 760 

« Ann. Phys. 28, 84 (1907). 

7 Ann. Phys. 37, 472 (1912). This paper also gives a large number of references to 
previous work. 



128 



Sorption of Gases at Low Pressures 



mm.) per 1 gm. charcoal (except where otherwise mentioned), 
and the temperatures are given in degrees on the absolute or 
Kelvin scale. (T = deg. C. +273) . 




Vo/umm p*r&t 



•£ and 760rt/fJ 



Fig. 55. Adsorption of Gases on Charcoal a'; 
Very Low Temperatures (Claude) 



G. Claude 8 has measured the adsorption of H 2 , He, Ne, 
and N 2 on charcoal at very low temperatures and low pressures. 
Table XVII gives the results obtained, which are shown graph- 
ically in Fig. 54. Curves I, II, and III show the data for He, 
Ne, and H 2 respectively, at T = 77.6, while Curve IV shows the 
data for N 2 at T = 90.6. The lower part of Fig. 54 shows Curves 
I and II plotted on a different scale. 

« Compt. rend. 158, 861 (1914). 



Sorption of Gases at Low Pressures 



129 



The adsorption of helium was observed to be extremely 
small, 0.21 cm. 3 being adsorbed at a pressure of 27 mm. 

It will be observed that although hydrogen has a lower 
boiling point than that of neon, the adsorptive power of charcoal 
for the latter is much lower than that for hydrogen. At very 
low pressures the amount adsorbed tends to become proportional 
to the pressure. For higher pressures, the form of the adsorption 
relation which has been used, as a general rule, is, 

v = k.pV* (51a) 

where 

v = volume of gas (measured under definite conditions) 
per unit weight of adsorbent. 

p = pressure. 
In this equation k and n are constants which depend on the 
nature of both the adsorbent and gas. Since this relation can be 
expressed in the form, 

log v = 7n log p + log k (51b) 

it is evident that if p and v are plotted on logarithmic paper, a 
straight line should be obtained whose slope gives the value of 
1/n. Fig. 55 shows Claude's data plotted in this manner. In 
this case, the value of 1/n is approximately unity, corresponding 
to a linear relation between p and v. At higher pressures and 
concentrations, the values of 1/n tend to decrease more and 
more. This is illustrated by Titoff's results 9 (see Table XVIII 
and Fig. 56) on the adsorption of various gases on coconut 
charcoal. 

TABLE XVII 



ADSORPTION 


OF GASES 


ON CHARCOAL (CU 


lude) 


NITROGEN 


(T =90.6) 


HYDROGEN 


(T=77.6) 


neon (T =77.6) 


P 


V 


P 


V 


P 


V 


0.004 


9.35 


0.006 


0.105 


0.45 


0.105 


0.010 


18.70 


0.0115 


0.21 


0.88 


0.21 


0.032 


37.4 


0.0205 


0.42 


1.30 


0.32 


0.088 


46.6 


0.036 


0.84 


1.74 


0.42 


0.385 


56.0 


0.083 


2.05 


3.50 


0.84 


1.107 


65.3 


0.176 


3.71 


5.30 


1.22 


11.50 


93.0 


0.475 


8.40 


7.20 


1.63 


33.2 


103. 


1.060 


14. 


11.30 


2.44 


90. 


112. 


3.50 


28. 


15.5 


3.25 


247. 


121. 


8.7 


42. 


19.4 


4.06 






20.6 


56. 


30.5 


6.18 






43.7 


63. 


40.5 


8.01 



• Loc. cit. 



ISO 



Sorption of Gases at Low Pressures 



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rH oq co -* »ot^ 



Sorption of Gases at Low Pressures 



131 



The effect of increased temperature in decreasing the 
adsorptive power is quite evident. The relative adsorption of 
different gases at the same pressure and different temperature is 
shown by the data given in Table XIX. 




O.OJ 



Fig. 56. 



QOZ 0.04 0.06 0.0X0.01 O.Z 04 06 0.8 JO 

Vo/ume Per GM. fO°C. and 760 MM.) 
Adsorption of Hydrogen and Nitrogen on Charcoal 
at Higher Temperatures (Claude) 



Miss Ida F. Homfray published in 1910 10 the results of 
quite an elaborate series of measurements on the adsorption on 
coconut shell charcoal of argon, nitrogen, carbon monoxide, 
carbon dioxide, methane and ethylene. 

The observations with the first four gases are shown graphi- 
cally in the curves given in Figs. 57 to 60. The temperatures are 
given in degrees absolute, and the volumes absorbed are referred to 
the constant weight, 2.964 gm., which was used in all experiments. 

The results for helium are of interest. 11 At the temperature 
of liquid air, the following absorption data were obtained : 



P (mm. of Mercury) 


V (Per gm. of Charcoal) in Cm. 3 


120. 


0.337 


171. 


0.465 


235. 


0.81 


427.6 


1.17 


705.0 


1.84 



l0 Zeits. physikal. Chem., 74, 129 (1910). 

u The adsorption of helium on charcoal has also been measured recently by S. McLean. 
Trans. Roy. Soc. Can. 12 (III), 79 (1918); Chem. Abst. IS. 1667 (1919). The amounts of 
helium adsorbed on charcoal at the temperature of liquid air were observed to be very small. 



132 



Sorption of Gases at Low Pressures 



TABLE XIX 
COMPARATIVE ADSORPTION OF DIFFERENT GASES (Titoff) 

At £ = 100 mm. 



Temperature 
(deg. Cent.) 


-79 


-23.5 





30 


80 


151.5 


Hydrogen 

Nitrogen 

Carbon Dioxide . 
Ammonia 


0.79 
15.89 

97.27* 


112.2 


0.227 
2.344 
30.41 
69.02 


1.178 
15.89 

29.24 


0.0607 
0.4688 
4.920 
7.96 


0.1633 

1.062 

2.77 



♦The temperature was —76.5 in this case, as CO2 solidifies at —79. 



The sorption of hydrogen by charcoal at temperature of 
liquid air has been specially investigated by J. B. Firth, 12 and 
J. W. McBain. 13 Both investigators have observed that equilib- 
rium is attained in this case only after a lapse of many hours. 
Most of the gas is apparently condensed instantaneously on the 
surface (true adsorption) . This is followed by a gradual diffusion 
of the hydrogen into the charcoal the rate of which obeys Fick's 
law of diffusion, as shown by McBain, and which must be re- 
garded as due to solution or occlusion of the gas in the charcoal. 
Firth finds that at equilibrium the relation between pressure and 
volume of gas adsorbed per unit weight of charcoal is not given 
by a linear relation, but by an equation of the form 

Table XX gives the equilibrium data observed. The pres- 
sures are given in mm. of mercury, and V gives the volume 
adsorbed (corrected to deg. C, 760 mm.) per gm. charcoal. 




O JO ZO3O4O5O6O7OS0 9OJ00U0HO 
Perfume per 2. 964 6M. Charcot / 

Fig. 57. Adsorption of Argon on Charcoal (Homfray) 



"Zeits. physikal Chem. 86, 294 (1913). 

IS \.c\f r>«* 



1 Loc. Clt. 



Sorption of Gases at Low Pressures 



1SS 




JO 20 JO fO 50 60 70 SO 9010C1101Z01301401501€OJ7C1?01?OZOO 

Vo/ume per 2964 GM. Cfiarcoa.1 



Fig. 58. Adsorption of Nitrogen on Charcoal (Homfray) 




U200 
^JOO 



O JO 2030 4050 60 70 SO 90200110 J20B0MCJ501€0 
yo/ume per 2S& CM. Charcoal 



Fig. 59. Adsorption of Carbon Monoxide on Charcoal (Homfray) 




JO ZO '30 '40 SO '60 70 SO 90 100110120150 MO 

yo/u7ne pen 2. 964 6/t. Charcoa/ 
Fig. 60. Adsorption of Carbon Dioxide on Charcoal (Homfray) 

McBain on the other hand obtains the relation 
v = k p Yi 
which would point to the hydrogen being absorbed in the atomic 
condition. At a pressure of 19 mm. and the temperature of 
liquid air the amount of hydrogen taken up per gm. of charcoal 
is 4 cm. 3 (at deg. C. .and 760 mm.) which is much less than that 
observed by Firth. 



134 



Sorption of Gases at Low Pressures 



TABLE XX 

SORPTION OF HYDROGEN BY CHARCOAL AT THE 

TEMPERATURE OF LIQUID AIR (Firth) 



p 


V 


P 


V 


9 


2L5 


90 


59.3 


17 


32.1 


126 


63.1 


30 


46.5 


186 


69.2 


51 


53.3 


245 


76.0 


59 


56.0 







Use of Charcoal at Low Temperatures in High Vacuum Investigation 

The only comprehensive data in the literature on adsorption 
at very low temperatures and low pressures is that published by 
Claude, which was mentioned previously. From his data it is 
possible, assuming the linear relation to be valid down to very 
low pressures, to calculate the amounts of nitrogen and hydrogen 
that can be adsorbed on charcoal at equilibrium pressures below 
1 bar. Table XXI gives these amounts in terms of the volume 
measured at 1 bar pressure (and deg. Ci- 
table xxi 
ADSORPTION ON CHARCOAL AT LOW TEMPERATURES 
(Extrapolated from Claude's data) 



Hydrogen (T=77.6) 


Nitrogen (T=90.6) 


P (bars) 


v 


P (bars) 


V 


8. 


106,000 


5.3 


9,500,000 


1. 


13,250 


1 


1,800,000 


0.1 


1,325 


0.1 


180,000 


0.01 


133 


0.01 


18,000 


0.001 


13 


0.001 


1,800 



That is, at a pressure of 0.01 bar (which is a maximum pres- 
sure for the efficient operation of hot cathode high vacuum 
devices), 1 gram of charcoal (such as used by Claude) would 
clean up about 130 cm. 3 of hydrogen or 18,000 cm. 3 of nitrogen, 
from a pressure of 1 bar down to 0.01 bar. 

Woodrow 14 measured, with a Knudsen gauge, the amount of 
clean-up of different gases by charcoal at liquid air temperatures. 
Neither the volume of the apparatus nor weight of charcoal are 
given. The latter was heated under simultaneous evacuation 
till the pressure fell to 1.5 X10~ 6 mm. of mercury (2X10 -3 bar) 

"Phys. Rev. 4. 491 (1914). 



Sorption of Gases at Low Pressures 



13-5 



and hydrogen, oxygen, or nitrogen was then introduced at an 
initial pressure of about 0.65 bar. The rate of clean-up in each 
case as followed with the gauge is shown in the table: 

RATE OF CLEAN-UP BY CHARCOAL 







PRESSURE IN BARS 






Time 










Hydrogen 


Oxygen 


Nitrogen 







0.647 


0.667 


0.600 




5 sec. 




0.387 






10 sec. 




0.227 






1 min. 


0.613 


0.0027 


0.020 




5 min. 


0.547 


0.002 






20 min. 


0.387 








1 hr. 


0.253 




0.007 




3 hrs. 


0.180 


0.002 






10 hrs. 


0.180 


0.002 


0.007 



Miss M. Daly and the author have carried out some experi- 
ments in this laboratory on the adsorption of gases by charcoal 
at low temperatures. Specially activated products (see below), 
supplied by Dr. F. M. Dorsey, were used in this work. Pressures 
were determined by means of the ionization gauge, and the rate 
of clean-up observed of both hydrogen and residual" gases present 
after sealing off the pump. In the latter case the gauge and tube 
containing 5 gm. charcoal with a large bulb (total volume = 3000 
cm. 3 ) were well exhausted on the condensation pump, heating 
the charcoal for over an hour to 360 deg. C. After sealing this 
system off the pump, the pressure was measured, and then liquid 
air put on the charcoal. The pressures before cooling the latter, 
and after, were as follows : 



V 


Initial Pressure 
(bars) 


Final Pressure 


3000 cm. 3 1 0.022 
3000 cm. 3 0.036 
3000 cm. 3 0.92 


0.0004 
0.0004 
0.0006 



It may be noted that the sensitivity of the galvanometer 
used with the ionization gauge was such that 0.0004 bar was 
about the lowest pressure that could actually be measured. 

In carrying out experiments with hydrogen, the same appa- 
ratus was used, except that another side tube was sealed on in 
which was contained a small thin-walled glass pellet (volume of 
3 cm. 3 ) filled with hydrogen at a known pressure. After exhaust- 
ing the gauge, charcoal tube, and bulb, this system was sealed 
off, the hydrogen pellet broken by shaking, and the residual 



136 



Sorption of Gases at Low Pressures 



pressure observed after immersing the charcoal tube in liquid 
air. Five gms. of activated charcoal were used as in the previous 
experiments. The residual gas pressure was also measured before 
breaking the pellet. Table XXII shows some of the results 
obtained. 

In general it required about an hour to attain equilibrium. 
In accord with McBain's observations it was found that the ini- 
tial condensation was followed by a slow diffusion of gas 
into the charcoal. 

TABLE XXII 
CLEAN-UP OF HYDROGEN BY ACTIVATED CHARCOAL 

(M. Daly and S. Dushman) 



V 


Press. 

After 

Sealing Off 


Initial 
Press, of 
Hydrogen 


Final 

Press, at 

Room Temp. 


Press. 
At Liquid 
Air Temp. 


3025 
100 

3025 
100 


0.0180 bar 
0.104 bar 
0.022 bar 
0.28 bar 


0.31 bar 

8.64 bar 

8.33 bar 

17.7 bar 


0.014 

0.02 

2.0 

0.24 


0.0004 
0.0004 
0.15 
0.0016 



A certain fraction of this clean-up was no doubt due to the 
action of the gauge itself. As will be shown in the following 
chapter there is an electrical clean-up which occurs in all hot- 
cathode devices. Furthermore, in presence of a heated filament 
atomic hydrogen is formed which is cleaned up at the temperature 
of liquid air. A blank experiment carried out without the use of 
charcoal gave 

F = 340; pressure after seal off =1.60 bar. 

On breaking the hydrogen pellet, the pressure rose to 7 
bars; then fell, owing to clean-up by gauge, to 2 bars. Liquid 
air was put on the side tube and the pressure fell in the course 
of 6 hours to 0.16 bar. On removing the liquid air, the pressure 
came back to 1.2 bar. 

In the measurements with charcoal the gauge filaments 
were lighted only during the time necessary to take a pressure 
reading, so that any error due to clean-up in the gauge was 
certainly not very large. 

It is evident from these measurements that with a charcoal 
tube immersed in liquid air it is possible to adsorb appreciable 
volumes of hydrogen and obtain residual gas pressures of less 
than 0.0001 bar. 



» Proc. Roy. Soc. 78 (A) 9 (1907). 
'• Loc. cit. 



Sorption of Gases at Low Pressures 137 

Preparation of Charcoal. "Activated" Charcoal 

The methods of preparing coconut charcoal as used by M. 
W. Travers, 15 J. W. McBain 16 and others is as follows: The soft 
part is heated in a muffle furnace for several hours at just below a 
red heat until no more vapor is evolved ; then the temperature is 
raised to a dull red heat for 30 seconds. After introducing the 
charcoal into a tube (and before use as an adsorbent) it is heated 
to 440 deg. C. (bath of boiling sulphur) for several hours, in 
vacuo. 

As mentioned previously, and as is evident from a com- 
parison of the results on adsorption obtained by different experi- 
menters, the sorptive power of charcoal is influenced largely 
by its structure, that is, mainly the porosity. It was observed 
that charcoal from the shell of the coconut gave a much greater 
sorption per unit volume of charcoal than that obtained from 
less dense forms of wood. But a great stimulus to the investi- 
gation of the effect of structure of charcoal on its adsorbing power 
was provided during the recent war by the necessity of develop- 
ing a highly efficient absorbent for gas masks. As a result there 
was evolved a technique for the production of a specially active 
form of charcoal which will no doubt be of equal utility in the 
peaceful art of vacuum production. 17 

Lemon observed in 1915 that different samples of charcoal 
made from the same material (coconut shell) showed very wide 
variations in sorptive power. It was found that this was due 
to variations in heat treatment and that a considerable increase 
in sorptive power, "activation," could be produced by repeated 
evacuations at 650 deg. C, each evacuation being followed by an 
absorption of air at the temperature of liquid air. On the other 
hand, by treating the charcoal to between 800 deg. C. and 900 
deg. C. during evacuation, a decrease in sorptive power (de- 
activation) resulted. 

The theory was advanced that the successive absorptions 
of air oxidize non-volatile hydrocarbons present in the charcoal. 
As a result an air-process of activating charcoal was evolved 
which consisted essentially of the following operations: 18 

17 The results of the investigations on this subject carried out by the Chemical Warfare 
Service, U. S. A., have been published mainly in the following papers: 

A. B. Lamb. R. E. Wilson, and N. K. Chaney, Journ. Ind. and Eng. Chem. 11, 420. 

1919, on "Gas Mask Absorbents." 
F. M. Dorsey, ib. 11, 281, 1919, on the "Development of Activated Charcoal." 
H. B. Lemon, Phys. Rev. 14, 282, Oct., 1919. 
N. K. Chaney, Trans. Am. Electrochem. Soc, 36, 91 (1919). 

The writer is indebted to these publications for the information on the properties and 
preparation of activated charcoal. 

18 F. M. Dorsey, loc. cit. 



1S8 Sorption of Gases at Low Pressures 

1. Initial distillation of cracked coconut hulls to a tem- 
perature of 850 deg. C. to 900 deg. C, and 

2. "Air treating" this carbonized material, screened 6 to 
14 mesh, at 350 deg. C. to 400 deg. C, for a certain 
length of time. 

The essential characteristics of an active charcoal are: 19 

1. High and fine-grained porosity. 

2. The presence of amorphous base carbon. 

3. Freedom from adsorbed hydrocarbons. 

To secure these objects it is necessary to use dense woods, 
carry out the distillation at relatively low temperatures, and then 
oxidize the hydrocarbons without injuring the carbon base to 
any measurable extent. "The permissible range of temperatures 
for the latter operation is a relatively narrow one, only about 50 
to 75 deg." For air oxidation this lies between 350 and 450 deg. 
C. Subsequently a steam process of activation was adopted, 
and for this reaction the optimum temperature is between 800 
deg. and 1000 deg. C. Other methods of activation have been 
used in Europe. All these processes yield charcoal which is much 
more active than that obtained by the simple distillation process 
used at one time. 

' ' From a study of the slope of the vapor pressure curves of 
liquids adsorbed upon such charcoal, the indications are that the 
pores have, if a cylindrical form be assumed, an average diameter 
of about 5X10 -7 cm. On this basis, 1 cm. 3 of active charcoal 
would contain about 1000 sq. meters of surface." 

The density of activated charcoal from coconut shells is 
about 0.4. Hence 1 gm. would contain about 2500 sq. meters of 
surface. Assuming that the clean-up by charcoal is due to a 
condensation of gas molecules on the surface, and that the diam- 
eter of a hydrogen molecule is about 2 X 10 -8 cm., it would require 
approximately 2000 cm. 3 (measured at deg. C. and 760 mm.) 
to cover the surface of 1 gm. of charcoal. Compared with this 
the adsorptions obtained by Miss Homfray, Titoff and Firth, 
even at atmospheric pressure, are very low, which may be 
accounted for partly by the smaller porosity of the charcoal used 
by them. 

It is of interest in this connection to mention a theory regard- 
ing the structure of charcoal which has been advanced by N. K. 
Chaney. 17 According to this theory "elementary carbon (other 
than diamond and graphite) exists in two modifications, 'active' 
and 'inactive 1 or alpha and beta. All 'primary' amorphous 
carbon consists essentially of a stabilized complex of hydro- 

i» A. B. Lamb, R. E. Wilson and N. K. Chaney. loc. cit. 



Sorption of Gases at Low Pressures 189 

carbons, adsorbed on a base of 'active' or alpha carbon. The 
active modification is formed whenever carbon is deposited at 
relatively low temperatures by chemical or thermal decom- 
position of carbon-bearing materials; in general below 500 to 
600 deg. C. The inactive modification results from similar 
decomposition at higher temperatures, in general above 600 to 
700 deg. C. The temperature at which molecular carbon is set 
free is apparently the controlling factor in determining whether 
it is of the active or inactive variety." The active form is 
characterized by a very high specific adsorptive capacity for 
gases. Chaney distinguishes between the true adsorptive capac- 
ity characteristic of the active form and a capillary capacity in 
virtue of which gas is taken up in pores formed by the loosely 
bound structure which results in carbonization of any carbon- 
bearing material, and he differentiates these as follows: On 
saturating an adsorbent and then noting the rate at which the 
gas is removed, it is observed that the portion absorbed in capil- 
lary spaces is given off readily while that adsorbed specifically 
is given off very slowly. "The weight of gas retained, after 
rapid weight loss has ceased, called the ' retentivity ' of the 
adsorbent, is a measure, therefore, of the proportion of active 
carbon present, in a given weight of adsorbent. This test applied 
to < pre-war charcoals shows that their adsorptive capacity is 
almost wholly capillary and dependent upon the physical struc- 
ture left by distillation in the primary carbon. In general even 
this capacity is extremely small compared with present stand- 
ards." The observation made by McBain that the sorption of 
hydrogen by ordinary charcoal at low temperatures occurs in 
two stages finds an explanation from this point of view. The 
major portion of the gas is taken up very rapidly, while a 
residual portion requires quite an interval of time to condense. 

The problem in preparing active charcoal, according to 
Chaney, therefore consists in devising some method which will 
get rid of the hydrocarbons adsorbed specifically by the active 
carbon at the instant of formation. This adsorbed gas forms 
quite stable complexes with the carbon base and constitutes 
the product which he designates as primary carbon, "because 
it is the original product first occurring in low temperature 
distillation of carboniferous material." The methods of pre- 
paring active charcoal by oxidation with steam and other schemes 
therefore have for their purpose the removal of these adsorbed 
hydrocarbons. 

In discussing the mechanism of the capillary and specific 
adsorptions, Chaney remarks: "The simplest theoretical as- 



ll^O Sorption of Gases at Low Pressures 

sumption is that capillary adsorption is the filling of actual cells 
with liquid due to lowered surface tension, and dependent upon 
the size of capillaries, i.e., the physical structure of the absorbent 
only. The specific capacity has been assumed to represent a 
field of force — probably due to unsaturated valences — which 
is independent of a grosser physical structure of the absorbent, 
i.e., it represents adsorption on a plane surface." 

While the discussion of the theories of adsorption must be 
reserved for a subsequent chapter, it is well to point out here 
that Langmuir has advanced the view, which he supports with 
a great deal of evidence, that true adsorption consists in a con- 
densation of gas in a layer one atom deep on the surface of the 
adsorbent. As has been shown, the older data on adsorption of 
gases by charcoal is not in contradiction with this view. Regard- 
ing the sorption of gases by activated charcoal, Langmuir has 
pointed out 20 that "truly porous bodies, such as charcoal, prob- 
ably consist of atoms combined together in branching chains 
of great complexity. The fibers of cellulose from which charcoal 
is usually formed consist of practically endless groups of atoms 

H H H H 

-c-c-c-c- 


H H H H 

held together by primary valences in the direction of their length 
and by secondary valence in the transverse directions. When the 
hydrogen and oxygen atoms are driven out by heat, the carbon 
atoms for the most part remain in their chains, but a certain 
number of cross linkages occur between these chains. The 
porosity of the charcoal thus undoubtedly extends down to atomic 
dimensions. The unsaturated state of the remaining carbon 
atoms explains the practical impossibility of removing the last 
traces of oxygen and hydrogen from any form of amorphous 
carbon." 

"Hence," according to Langmuir, "it is evident that with a 
structure of this kind, it is meaningless to talk about the surface 
on which adsorption can take place." On plane surfaces the 
maximum adsorption would correspond to a layer one molecule 
deep; but in the case of charcoal, there is no definite surface 
which can be covered by a unimolecular layer. The atoms of 
carbon would be separated by spaces which might hold one or 
more molecules of the gas, and on the other hand, these spaces 
might be too small to hold even one molecule. 

!0 J. Am. Chem. Soc. S8, 2221 (1916). 



Sorption of Gases at Low Pressures 141 

It will be observed that Chaney agrees with Langmuir in 
concluding that the specific absorptive capacity of activated 
charcoal is a measure of the amount of gas condensed as a uni- 
molecular layer. 

H. Briggs, 21 as a result of his investigations on the adsorp- 
tion of gas on charcoal and silica gel, concludes that while the 
chemical character of a material affects its properties as a gas- 
adsorbent, there are, with any given material, two factors which 
also influence the adsorptive power, viz.: "(a) the degree of 
canalisation of the substance, i.e., its porosity on the microscopic 
or ultramicroscopic scale, and (b) the degree of porosity on the 
molar scale." From the measurements on the size of the pores 
made by Lamb, Wilson and Chaney, 17 which have already been 
mentioned. Briggs infers that "the greater part of the 
internal gaseous space of an efficient adsorbent consists of pas- 
sages which are not greatly larger than the gas molecules." 
According to his view, Chaney's assumption of the existence of 
two allotropic forms in active charcoal is not sufficiently sup- 
ported by the experimental evidence, and he concludes that the 
efficiency of activated charcoal is due to the presence of the 
molar interstices. 

H. H. Sheldon 22 has shown that while ordinarily nitrogen 
is more readily adsorbed on charcoal than hydrogen, it is possible 
by suitable treatment to produce a charcoal in which the relative 
adsorptive capacities for the two gases are reversed. He has 
also observed that evacuation of charcoal at 600 degrees C. 
followed by adsorption of oxygen at low temperatures and this 
again by re-evacuations at the higher temperature, leads to con- 
siderable improvement in the adsorptive capacity of charcoal. 

J. C. Philips, S. Dunnill and O. Warkman 23 have made 
similar observations with wood-charcoal. The greater the 
facilities for the access of air to the material during heating, the 
greater the resulting increase that was obtained in the sorptive 
power. They also observed that the increased activity was 
accompanied by a decrease in bulk density, indicating, according 
to Briggs, an increasing degree of "molar" porosity. 

These observations are in accord with results obtained in 
this laboratory. A given sample of charcoal shows marked 
improvements as a clean-up reagent in high vacuum work, after 
it has been evacuated and saturated with gas several times in 
succession. 



» Proc. Roy. Soc. (London) 100. 88 (1921). 
« Phys. Rev. 16, 165 (1920). 
"Trans. Chem. Soc, 117. 362 (1920). 



14% Sorption of Gases at Low Pressures 

As mentioned previously, the results obtained in this laboratory 
by the use of activated charcoal in high vacuum investigations 
have been very encouraging. It is well, however, to point out, 
as has been done by Briggs, that from data obtained on the 
adsorptive capacity of an adsorbent at higher pressures, it is 
not at all safe to predict the behavior at lower pressures. At 
higher pressures and low temperatures where most gases are 
near their liquefaction conditions, the attraction between mole- 
cules of the gas is much stronger than that between the mole- 
cules in the gas and those at the surface of the solid. The con- 
trary is, however, true at very low pressures. 24 

(II) ABSORPTION OF HYDROGEN BY PALLADIUM BLACK 
Absorption Relations 

Palladium, on being heated, allows hydrogen to pass through 
it quite freely. This observation was utilized in early forms of 
gas-filled X-ray tubes to soften tubes which became hard because 
of electrical clean-up. Further investigation has shown that the 
phenomenon is due to the absorption of hydrogen which then 
diffuses through the metal into the tube. 

This absorption of hydrogen by palladium has been studied 
by a number of investigators. Hoitsema 25 found that at 
temperatures above 100 deg. C, the absorption law is 

v = k \/p 
where v denotes the volume absorbed per unit weight and p is 
the pressure. This indicates that the hydrogen is occluded in 
the atomic condition. The absorption was measured at pres- 
sures ranging from 1 to 5000 mm. and at temperatures from 
deg. to 250 deg. C. The results have therefore no bearing on 
the utility of palladium as an absorbent at low pressures and low 
temperatures. It may be stated that both metal foil and palla- 
dium black (described later) were used in this investigation. 

A. Sieverts 26 has also investigated the behavior of hydrogen 
and palladium (wire, foil and "black"), with a view to evolving 
a satisfactory theory of the phenomenon. He considers that the 

24 Although not bearing directly on the topic of this discussion, it is of interest to observe 
that the selective sorption of different gases by charcoal may be used for the purification 
of gases. Thus, where it is desirable to obtain pure helium, charcoal in liquid air maybe 
used to adsorb impurities such as nitrogen, oxygen and even hydrogen. Similarly the latter 
gas may be freed of traces of nitrogen and oxygen. In this connection the following recent 
publications may be consulted: 

(1) H. B. Lemon and K. Blodgett. Studies of the Absorption of Gases by Charcoal. 

Phys. Rev. 14, 394 (1920). 

(2) R. E. Wilson. Note on the Adsorption of Nitrogen and Oxygen on Charcoal. 

Phys. Rev. 16, 8 (1920). 
« Zeits. physikal. Chem. 17 (1895). 

* Zeits. physikal. Chem. 88, 103 and 4.51 (1914). This paper contains numerous references 
to previous literature. 



Sorption of Gases at Low Pressures 



143 



absorption is a true case of solution. The range of pressures used 
was from 1 to 760 mm. and the solubility determinations were 
carried up to temperatures as high as 820 deg. C. The solubility 
was found to vary with the nature of the sample used. At higher 
pressures, the relation 

v = k\Z~p-\-k 2 p 
was found to be more in accord with the data. This relation was 
obtained for all the samples. 

A. Holt, E. C. Edgar and J. B. Firth 27 have concluded that 
palladium can exist in the form of both active and inactive modi- 
fications, as far as absorption is concerned, and the activity of 
any sample decreases with time. By heating (in hydrogen) the 
absorbing power can be revived. Furthermore, palladium shows 
phenomena of diffusion similar to those observed by McBain 
in the case of hydrogen and charcoal. 

S. Valentiner has carried out a series of measurements on the 
absorption of hydrogen at relatively low pressures. 28 The results 
obtained were not very satisfactory. At the same equilibrium 
pressure it was found possible to absorb amounts of gas which 
differed for different samples. Apparently the absorbing power 
varies not only with the degree of fineness of the palladium black 
but also with its subsequent heat treatment during evacuation. 
Some of the data obtained by Valentiner are tabulated in Table 
XXIII. The remarkable increase in absorptive power at —190 
deg. C. is quite evident, although the actual absorptions for the 
same equilibrium pressure vary widely. In the table, P gives 
the pressure in mm. of mercury, and V the volume at standard 
pressure and temperature per gm. of palladium black. 

TABLE XXIII 

ABSORPTION OF HYDROGEN BY PALLADIUM BLACK 

(Valentiner) 



TEMP. 


= 20° c. 


TEMP. = 


=20° c. 


TEMP. = 


= 1900 c. 


P 


V 


P 


V 


P 


V 


0.001 


0.10 


0.014 


0.27 


0.0005 


2.05 


0.005 


0.26 


0.031 


0.33 


0.0015 


2.11 


0.037 


0.40 


0.056 


0.37 


0.001 


3.06 


0.110 


0.52 


0.087 


0.41 


0.001 


9.1 


0.190 


0.59 


0.184 


0.49 


-0.002 


33.0 


0.315 


0.70 


0.30 


0.55 


0.005 


40.0 


0.52 


0.82 


0.52 


0.61 


0.012 


47.2 


0.76 


0.92 


0.88 


0.67 


0.025 


63.0 



*> Zeits. physikal. Chem. 82, 513 (1913). 

« Vcrh. d. deutsch. physikal. Ges. S, 1003 (1911). 



144 Sorption of Gases at Low Pressures 

Compared with the adsorption of hydrogen on charcoal 
(Claude's data, Table XVII), the absorption by palladium at 
liquid air temperature is observed to be much greater. 

Preparation of Palladium Black 

The method of preparation has been described by Hoit- 
sema. With slight variation this method has been used in this 
laboratory as follows: The palladium in the form of sheet or 
wire is dissolved in aqua regia, evaporated on a water bath till 
acid vapors have disappeared; the solution is then diluted, 
warmed, and concentrated solution of sodium carbonate added 
to neutralize free acid. A slight amount of acetic acid is then 
added, the solution is warmed, and a warm concentrated solution 
of sodium formate added. The palladium comes down as a black 
flocculent precipitate which settles rapidly at the bottom of the 
breaker. The supernatant liquid is decanted, and the precipitate 
washed with distilled water till the wash water shows no traces 
of chlorides. The palladium "black" is then washed with 
alcohol and transferred to a U-tube, where it is dried by blowing 
air over it and then evacuated on a rough pump. The U-tube 
ought to have side tubes through which gas can be passed and 
constrictions at which it can be sealed off later. After the rough 
evacuation (with slight warming of the U-tube), hydrogen is 
passed over the palladium black for some time, and while the gas 
is still passing through the tube the latter is sealed off at the con- 
strictions. This leaves the palladium black in equilibrium with 
hydrogen and it can be kept active for a long time. 

For use in exhaust work, the U-tube is opened and a sample 
transferred to a tube such as is used in the case of charcoal. It 
is well to cover the top of the palladium black with glass wool 
in order to prevent it from being drawn into the rest of the appa- 
ratus when vacuum is applied. 

Experiments on the Use of Palladium Black in the Production of High 
Vacua 

A number of experiments have been carried out in this 
laboratory by A. G. Huntley, Miss M. Daly. and .S. Dush- 
man. While the behavior of palladium black was found to be 
extremely erratic, the results obtained showed that it is possible 
to obtain samples which possess very high absorbing power. 

An ionization gauge with an appendix containing about 1 
gm. of palladium black was well exhausted on a condensation 
pump and sealed off at a residual gas pressure of about 0.2 bar 
(the gas consisting probably of nitrogen and hydrogen). On 



Sorption of Gases at Low Pressures 1^5 

immersing the appendix in liquid air, the pressure decreased to 
0.004 bar with the gauge filament lighted. On turning off the 
filament for some time, and then lighting it for an instant, the 
pressure was observed to have decreased still further to 0.0005 
bar. Apparently, there is a continual slight evolution of gas 
from the walls of the gauge and filament leads even after the 
metal parts have been bombarded for a long time. In other 
experiments pressures as low as 0.0001 bar were obtained in a 
sealed off gauge with a palladium tube immersed in liquid air. 

A number of experiments were carried out using palladium 
black for absorbing the residual gases in a small kenotron ex- 
hausted on an oil pump only. An ordinary lamp exhaust system 
was used giving an exhaust pressure of about 1 bar. A few 
milligrams of palladium black were placed in a kenotron (about 
100 cm. 3 volume) which contained a 6-volt 2.5-ampere tungsten 
filament and a cylindrical molybdenum anode about J€ m - m 
diameter by % in. in length. The tube was exhausted on the 
oil pump, with simultaneous heating in an oven for 30 minutes 
at 360 deg. C, and sealed off. The metal cylinder was then 
bombarded to a white heat by making the filament cathode. 
The gases evolved were absorbed rapidly by the palladium black, 
in spite of its being above room temperature, and finally the 
vacuum became so good that excellent space charge character- 
istics were obtained. Special experiments showed that in order 
to obtain this condition the pressure must be at least as low as 
0.05 bar. Thus even with a few milligrams of palladium black 
at room temperature it was possible to clean up appreciable 
quantities of gas. Similar results were obtained time after time. 
In fact a large number of small kenotrons and pliotrons were 
exhausted in this manner with the regular exhaust system used 
in, lamp factories, and without having to use a condensation 
pump or liquid air. 

As subsequent investigation showed that the same results 
could be obtained with the very much cheaper activated char- 
coal, and furthermore, as some samples of palladium black 
absolutely failed for some undetermined reason to act as absorb- 
ent, this method was used for only a short time. The results, 
however, suggest interesting possibilities in the production of 
high vacua by means of palladium black and further investiga- 
tion ought to be carried out with a view to determining definitely 
the conditions under which it can be made active. It has been 
recently shown by E. B. Maxted 29 that hydrogen sulphide 
inhibits the absorbing efficiency of palladium black. Similar 



146 Sorption of Gases at Low Pressures 

facts have been known for a long time in the case of various 
metallic catalysts, and probably the same causes influence the 
behavior of palladium black. 



III. SORPTION OF GASES BY GLASS, METALS 
AND OTHER SUBSTANCES 

Sorption of Gases. General Remarks 

From the standpoint of high vacuum technique, the phe- 
nomena included under the generic term "sorption" are of 
importance in indicating what methods may be applied to clean 
up the residual gases in sealed-off devices. The usual gases 
present in such cases are hydrogen, oxygen, nitrogen, carbon 
monoxide, carbon dioxide, and water vapor. Inasmuch as the 
vessels to be exhausted ordinarily consist of glass and also have 
metal parts, it is furthermore of importance to consider the 
behavior of different kinds of glass and metals with respect to 
sorption and evolution of gas. 

In the case of charcoal and palladium black, discussed pre- 
viously, the initially evacuated adsorbent takes up a portion of the 
gas with which it is in contact and the distribution of gas between 
the adsorbent and the gas phase depends not only upon the 
temperature of the former but also upon the initial total amount 
of gas present. Furthermore, different gases are adsorbed to a 
widely different extent on the same adsorbent as has already been 
illustrated in the case of charcoal. A similar statement holds 
true for the adsorption of the same gas on different adsorbents. 
Table XXIV taken from Freundlich 30 gives a comparison between 
the behavior of wood charcoal, meerschaum, and glass powder as 
adsorbents. 

While the adsorption of gases on charcoal has been studied 
extensively because this substance is such a powerful adsorbent 
for most gases, especially at very low temperatures, many other 
substances have also been found to exhibit the same property. 
Meerschaum, powdered glass, silica, alumina, glass wool, thoria, 
and other substances in a finely divided state have been used as 
adsorbents in special cases. The gel of silicic acid has been 
studied with respect to its adsorbing power for SO2 31 and also 



» Journ. Chem. Soc. 115, 1050 (1919). 
>° Kapillarchemie, 1909. p. 97. 

« J. McGavack, Jr.. and W. A. Patrick, J. Am. Chem. Soc. 42, 946 (1920). W. A. Patrick. 
Chem. and Met. Engr. 22, 949 (1920). 



Sorption of Gases at Low Pressures 



U? 



for N 2 and H 2 . 32 Merton 33 has observed that finely divided 
copper, obtained by reducing a solution of a copper salt, adsorbs 
hydrocarbons, nitrogen, and hydrogen with great rapidity. 
The copper should be heated to a temperature not exceeding 
250 deg. C. It gradually loses its adsorbing power with use, but 
Merton finds that it can be used to clean up the residual gas, 
after exhausting with an oil pump, to such a low pressure that 
the space becomes "non-conducting." 



TABLE XXIV 
ADSORPTION OF GASES ON DIFFERENT ADSORBENTS 



Adsorbent 


Gas 


Vol. Adsorbed at 

100 mm. Hg. and 

deg. C. 


Wood charcoal 

Meerschaum 


CQ 2 
NH 3 
S0 2 
CH3CI 

NH 3 

S0 2 
CH3CI 

C0 2 
NH 3 
S0 2 


24.9 cm 3 /gm. 

95.1 

73.6 

57.7 

84.5 


Glass powder 


24.3 
27.1 

1 
9 
6 



In general, adsorbed gases are re-evolved on heating the 
adsorbent; that is, the reaction is reversible or practically so. 
The sorption of oxygen by charcoal and the metals platinum and 
palladium is, however, not of a similar nature. The behavior of 
charcoal in contact with oxygen has been studied by a number of 
investigators. When charcoal which has adsorbed oxygen is 
heated, only a portion of the gas is recovered as oxygen, the 
remainder is re-evolved as carbon monoxide and dioxide. The 
results of the most recent investigation of this subject, by H. H. 
Lowry and G. A. Hulett, 34 lead to the conclusion that while 
some of the oxygen is adsorbed on the surface of the charcoal 
and may be recovered by heating, the rest is held by the charcoal 
as a surface compound or compounds, which are stable at 
ordinary temperatures but which break down to CO and CO2 at 
200 deg. C. and above. 

82 H. Briggs, loc. cit. He has also shown how the adsorption capacity of silica gel is 
affected by heat treatment. 

« J. Chem. Soc. London, 105, 645 (1914). 

84 J. Am. Chem. Soc. U2, 1408 (1920). This paper gives a large number of references to 
previous literature on this subject. 



llf.8 Sorption of Gases at Low Pressures 

Platinum black (prepared in a manner similar to that used 
for palladium black) can take up more than 800 times its volume 
of oxygen. This oxygen is removed with great difficulty, show- 
ing that the adsorption is not a reversible phenomenon. Here 
again, the conclusion has been drawn that PtO is formed on the 
surface. 35 It will be shown in a subsequent connection that in 
reality these adsorption phenomena are probably not essentially 
different from the ordinary reversible cases of adsorption. 

Sorption of Gases by Metals 

A survey of the results obtained by a large number of in- 
vestigators shows that the sorption phenomena of gases by 
metals are of quite a complex nature. 36 Not only do we have 
cases of true adsorption, but also cases in which the gases are 
dissolved in the metals and behave in every way like solutions, 
and still other cases in which, undoubtedly, stable chemical 
compounds are formed either on the surface or throughout the 
body of the metal, and in some cases we do not yet understand 
the exact mechanism of the reaction. As will be pointed out in 
the discussion of theories of adsorption, we are dealing in such 
cases with phenomena which are in the "No-man's" land that 
exists between so-called physical and chemical reactions. It has 
therefore been considered best to discuss in this section all those 
cases in which there is an absorption of gases by solids. The 
behavior of hydrogen with respect to different metals illustrates 
all these cases very well and is of special interest from the point 
of view of vacuum investigations. 

The sorption of hydrogen by palladium black has been 
discussed already. At low temperatures the evidence points to 
the conclusion that we are dealing with a case of adsorption or 
surface condensation. On the other hand, there is also very good 
proof that, at higher temperatures at least, hydrogen dissolves 
in palladium in the atomic condition. The same conclusions hold 
for hydrogen and platinum. The latter, in the condition of 
platinum black, is able to take up about 100 times its volume of 
gas. 37 As a clean-up agent for residual gas in vacuum devices, 
platinum black is less efficient than palladium black. 

An investigation on the behavior of hydrogen towards 
platinum and iridium has been carried out by A. Gutbier and his 
associates. 38 The results show that the maximum of absorption 

15 Engler and Woehler, Zeits. f. anorg. Chem. 29, 1 (1902). Mond, Ramsay, and Shields, 
Zeits. f. physikal. Chem. 25, 657 (1898). 

36 For a general summary of the literature, see Trans. Faraday Soc. H, 173, 232 (1919). 
87 For literature see Bancroft, Jour. Franklin Inst., 185, 29 (1918). 
" Ber. d. deutsch. Chem. Ges. 52B. 1366-74 (1919). 



Sorption of Gases at Low Pressures 



149 



by platinum black occurs at deg. C, while in the case of iridium 
black the maximum occurs at 20 deg. C. While the former was 
observed to absorb as much as 160 volumes hydrogen, platinum 
sponge only absorbs 1 volume. The sorptive capacity of 
iridium was also observed to be much less than that of platinum. 
The behavior of hydrogen in contact with tantalum is similar 
in certain respects to the foregoing phenomena. Pirani 39 has 
observed that this metal when heated in hydrogen can occlude 
about 740 times its volume of the gas. On subsequent heating 
in a vacuum about 550 volumes are given off, while the rest of 
the gas is removed only at the melting point of the metal. The 
occluded hydrogen makes a tantalum filament quite brittle and 
the electrical resistance is increased considerably. 40 



TABLE XXV 
WEIGHT OF H 2 IN mg. DISSOLVED BY 100 g. TANTALUM 

AT 760 mm. 



deg. C. 


mg. 


deg. C. 


mg. 


100 


400 


630 


51.2 


183 


377 


730 


33.4 


263 


327 


830 


20.3 


314 


297 


980 


14.9 


474 


157 


1030 


11.9 


530 


107 


1130 


9.6 






1230 


8.0 



A more careful investigation of the sorption of hydrogen by 
tantalum was carried out by A. Sieverts and E. Bergner. 41 They 
observed that the amount of gas taken up by the metal decreases 
with increase in temperature (as in the case of hydrogen and 
palladium), and that a wire heated to 1200 deg. C. in vacuo 
absorbs hydrogen slowly at temperatures above 500 deg. How- 
ever, once the wire is saturated with gas at the higher tem- 
peratures, it absorbs very much more easily at lower temper- 
atures. At ordinary pressures, the amount of gas taken up is 
given by the relation 

v = k m\/~p 
where m — weight of tantalum 

p = pressure of hydrogen . 
Thus, as in the case of palladium, we must conclude that the 
hydrogen in the metal is in the atomic condition. The solubilities 

» Zeits. f. Elektrochem, 11, 555 (1905). 

*° Similar effects of adsorbed gases on the resistance of carbon filaments have also been 
observed by K. Sickel, Z. f. Physik. 4. 288 (1921). 
« Ber. d. deutsch. Chem. Ges. U, 2394 (1911). 



150 



Sorption of Gases at Low Pressures 






for different temperatures are given in Table XXV. At very 
low pressures the solubility is less than that calculated by the 
foregoing relation. 

The same investigators also observed that hydrogen is 
absorbed by tungsten to a very negligible extent. 




zoo 



400 GOO 800 1000 1200 1400 1600 
Degree 3 -C. 



Fig. 61. Solubility of Hydrogen in Copper, 
Iron and Nickel 



In the case of the metals, copper, iron, and nickel, the care- 
ful investigations of A. Sieverts and his associates 42 have shown 
that the amount of hydrogen dissolved at any given temperature 
varies with the pressure according to the relation 

V = Wp 
which indicates that the hydrogen is present in solution in the 
atomic condition. Furthermore the amount of gas taken up 
depends only upon the mass of the metal and not its area (as 
distinguished from adsorption). Also the solubility increases 
with the temperature, whereas in all cases of adsorption the 
amount of gas taken up decreases with increase in temperature. 
Fig. 61 gives for comparison the solubilities of hydrogen in each 
of the above metals. It will be observed that nickel is capable 

« Zeits. f . physikal. Chem. 77, 591 (1911). 



Sorption of Gases at Low Pressures 



151 



of dissolving appreciable amounts of the gas at higher tem- 
peratures. At the melting point, the solubility increases abruptly 
as shown by the vertical dotted lines on the curves for nickel 
and iron, and under these conditions the former is capable of dis- 
solving twelve times its volume of hydrogen. If the metal satu- 
rated with gas at a higher temperature is cooled very rapidly, 
amounts are retained which are very much larger than those 
corresponding to equilibrium at the lower temperature. These 
observations are of great importance as a guide to the com- 
position of the gases which may be evolved from metal parts 
used in vacuum apparatus. 

The equilibrium between metal and gas is attained at a 
slower rate, the lower the temperature. Hence, it is necessary 
to heat metals in a vacuum to as high a temperature as they can 
stand in order to free them thoroughly of dissolved gases. 

TABLE XXVI 

DISSOCIATION PRESSURES IN mm. Hg OF POTASSIUM 
AND SODIUM HYDRIDES 



deg. C. 


KH 


NaH 


290 




5.01 


300 


7.3 


8.02 


320 


17.62 


18.62 


340 


39.8 


41.98 


360 


85.9 


90.66 


380 


177.0 


181.97 


400 


592.74 


354.8 



The metals of the alkali and alkaline earth group combine 
chemically with hydrogen to form hydrides. Sodium absorbs 
hydrogen at temperatures above 300 deg. C. and forms the com- 
pound NaH. Similarly, metallic calcium combines rapidly with 
hydrogen at a dull red heat to form CaH 2 . 

The dissociation pressures of NaH and KH have been 
measured by F. G. Keyes. 43 Table XXVI gives a few of the data 
obtained at higher pressures. Extrapolating from these we 
obtain for the dissociation pressure of KH at lower temperatures 
the following values : 



«U. Am. Chem. Soc. 34. 779 (1913). 



152 Sorption of Gases at Low Pressures 



deg. C. 


press, in mm. 


100 

27 


7.76X10- 6 
6.84 X10" 10 



That is, potassium ought to clean up hydrogen to a residual 
equilibrium pressure of less than 10~ 6 bar. The dissociation 
pressure of CaH 2 and the other hydrides of the alkaline earth 
group have not been determined. 

Similarly some of the rare earth elements, like lanthanum 
and cerium, absorb hydrogen very rapidly at a temperature of 
about 250 deg. C. While Moissan and others claim the existence 
of compounds like LaH 3 , other investigators believe that we 
have in these cases solid solutions of hydrogen in the metals. 
Smith 44 classifies the combinations between hydrogen and metals 
into three classes: 

Compounds Class 1. Hydrogen acts as a base, e.g., H 3 Sb, 
H 3 As, etc. 

Compounds Class 2. Hydrogen acts as an acid, e.g., CaH 2 , 
NaH, etc. 

Class 3. Sorption compounds, e.g., palladium hydride, 
solutions of hydrogen in copper, etc. 

With regard to a number of metals, the exact nature of the 
reaction with hydrogen seems very doubtful. Of the metals of 
the rare earth group, thorium, neodymium, praesodymium, and 
samarium appear to absorb measurable quantities of hydrogen, 
and Smith assigns these to Class 3, while other investigators 
assume the actual formation of hydrides. Uranium absorbs 
hydrogen to a slight extent, while tungsten, molybdenum, and 
iridium absorb little or none at all. 

The writer had occasion some time ago to try some experi- 
ments on the adsorption of hydrogen by films of tungsten and 
iron deposited in vacuo on glass. In neither case could any clean 
up of hydrogen be determined. On the other hand, Heald 45 has 
observed that films obtained by cathodic sputtering (with high 
voltage) of cadmium, silver, and steel showed marked sorption of 
hydrogen. 

** For a general survey of the literature on the subject of hydrogen sorption by metals,, 
reference may be made to the paper by Donald P. Smith, ' 'The Occlusion of Hydrogen by 
the Metallic Elements and Its Relation to Magnetic Properties," Journ. Physical Chem., 
23, 186 (1919); J. H. Andrew (Trans. Far. Soc. 14, 232, 1919) has advanced the theory that 
the occlusion of hydrogen by Pd and Fe is due to the presence of an active, amorphous phase 
of the metal. A. Gutbier (Ber. 52 B, 1366—74. 1919) has investigated the behavior of hydro- 
gen towards iridium and platinum. Iridium absorbs hydrogen only slightly. Platinum black 
has the maximum absorptive power at deg. C, corresponding to 160 volumes of Hj. 

« Phys. Rev. 24, 269 (1907). 



Sorption of Gases at Low Pressures 153 

On the whole, it can be stated in the light of the present 
information that while a number of metals take up hydrogen to 
a larger or smaller extent, palladium and platinum black are the 
only metals which are known with certainty to clean up sufficient 
gas to make them of value in vacuum work. 

Still less is known of the behavior of other gases with respect 
to metals. We know that some metals, like those of the alkali 
and alkaline earth group, also thorium, form nitrides on heating 
them in contact with nitrogen, but there are very few published 
data on which to base any conclusion as to whether such reactions 
can be used in cleaning up nitrogen gas in vacuum work. 

An interesting method for removing residual gases based on 
the reaction between these gases and thorium (or zirconium) 
at higher temperatures has been suggested by W. D. Coolidge. 46 
"The use of the metals calcium, magnesium, sodium, and 
potassium," he states, "has been suggested for the chemical 
removal of (residual) gases. However, the high vapor pressure 
of these metals offers a serious drawback to their use for all 
purposes and particularly for certain types of electrical appa- 
ratus, having a very high vacuum. On the other hand, the metals 
of the rare earth group, having a low vapor pressure, particularly 
thorium and zirconium, are peculiarly well suited for the removal 
of gases capable of chemical combination, such as oxygen, nitro- 
gen, hydrogen, water vapor, the oxides of carbon, and the like. 
These metals form by combination with these gases chemically 
stable compounds of low vapor pressure." 

Coolidge uses the metal in the form of a very fine powder. 
After having first exhausted the tube or bulb in the usual manner 
(and after all metal parts have been heated to a high temperature) 
dry air or nitrogen is admitted and powder introduced from a side 
tube. The bulb is then re-evacuated, sealed off the pump, and 
the glass heated at the point where the powder is situated. 
"The metal will be observed to glow as a reaction takes place 
and the result is a vacuum so high that no gas ionization effects 
can be observed when an electron current is transmitted" (as in 
a hot cathode device). 

In a similar manner, H. Huthsteiner and the author have 
observed that a clean copper filament treated in oxygen at low 
pressure will clean up the gas very rapidly and in large amounts. 
Apparently the oxygen is able to diffuse into the metal and thus 
converts it gradually into Cu 2 0. On the other hand, some recent 
experiments by C. A. Kidner and the author have shown that 

« Patent No. 1, 323. 386, Dec. 2, 1919. 



154 Sorption of Gases at Low Pressures 

a freshly formed calcium film obtained by volatilizing the metal 
in vacuo does not absorb either oxygen or hydrogen, reactions 
which one would naturally assume ought to occur very rapidly. 
The investigations of Langmuir on the clean up of gases by 
volatilizing tungsten and molybdenum filaments and of Soddy on 
the clean up of gases by volatilizing calcium (barium, or stron- 
tium) have yielded important results. In view, however, of the 
radically different nature of the reactions studied, the discussion 
of these must be deferred to the following chapter. 

Adsorption of Water Vapor 

The problem of completely removing absorbed or dissolved 
water vapor from the walls of glass vessels is one of the most 
important in vacuum work. The sorption of water vapor by 
glass surfaces has therefore been studied by a large number of 
investigators. Closely allied with this is the problem as to the 
amounts of water vapor and other gases which are evolved from 
glass vessels under definite temperature conditions. 

In one of the first investigations on this subject, 47 Bunsen 
observed that even at very high temperatures (500 deg. C.) 
silicates (chemically analogous to glass) retain appreciable 
amounts of water vapor. The total amount of water liberated 
from 2.11 sq. meters of glass surface which had previously been 
dried thoroughly at 20 deg. C. was 22.3 mgm. "Warburg and 
Ihmori 48 found that measurable amounts of water vapor were 
condensed upon the surface of freshly blown glass bulbs and of 
bulbs which had not been thoroughly washed. After washing 
or boiling these glass surfaces and then thoroughly drying, no 
adsorption of water vapor could be detected." 49 L. J. Briggs 
measured the sorption of water vapor by quartz powder. Fifty 
grams were used having a superficial area of 2.0 sq. meters. 
The amounts taken up at different pressures of water vapor at 
30 deg. C, were as follows: 



VAPOR 


WATER ADSORBED* 


Press, mm. Hg. 


mgm. 


26.1 


9.0 


19.6 


4.6 


0.2 


0.5 


10.7 


2.9 


31.4 


26.7 



* Average of two or more experiments. 



« Wied. Ann. 20, 545 (1883); 24, 321 (1885). 
«» Wied. Ann. 27, 481 (1886); SI, 1006 (1887). 

«• Quoted from the paper by L. J. Briggs, Journ. Physical Chem. 9. 617 (1905), on th« 
'Adsorption of Water Vapor by Quartz." 



Sorption of Gases at Low Pressures 155 

The last two values were obtained with samples which had 
previously been dried to constant weight at 110 deg. C. 

The sorption of water vapor by charcoal has also been in- 
vestigated by H. H. Lowry and G. A. Hulett. 50 At a pressure 
of 23.4 mm. and 29.9 deg. C, as much as 783.1 mgm. of water 
were taken up per gm. of charcoal (estimated area of surface, 
300 sq. meters), corresponding to 2.6 mgm. per sq. meter. They 
conclude that "water vapor is not adsorbed, but is held by 
capillary action." 

The sorption of water vapor by pulverized synthetic quartz 
and anorthite has been studied by J. R. Katz. 51 "The amount 
of water taken up reaches a fairly definite limit when the vapor 
pressure of the water is about 0.7 of the saturated vapor. The 
quantities of water adsorbed per sq. cm. of surface under these 
conditions were 1.3 X10 -6 gm. for quartz and 6.2X10 -6 gm. for 
anorthite. These correspond to layers of water 13 and 204 mole- 
cules deep, respectively." 

The result obtained by Briggs for the amount taken up by 
quartz at 31.4 mm. pressure corresponds to a film 2.66 X10 -6 cm. 
thick or about 50 molecules deep. 

Similar results have been obtained, as will be mentioned 
below, by Langmuir in studying the gases evolved from glass 
bulbs. There is no doubt, however, that in all those cases, 
where apparently the layer of adsorbed gas is more than one or 
two molecules in thickness, we are not dealing with a true adsorp- 
tion phenomenon. According to Langmuir, the sorption by glass 
is to be regarded as a process of solution of the water in the glass, 
in much the same manner as we know is the case in the absorp- 
tion of moisture by sodium silicate and gels. It is also quite 
possible that in the case of powders the moisture may be actually 
condensed as a liquid in fine capillary spaces between the grains. 
Bancroft 52 mentions a number of cases in which very fine powders 
apparently have appreciable films of air or other gases surround- 
ing each small particle. Thus a liter of carbon black may con- 
tain 2.5 liters of air, and it has been observed that "a rock 
powder which would pass through a 200-mesh sieve surged like a 
liquid." 

The presence of such relatively large amounts of water 
vapor on glass surfaces and even metal surfaces (as observed 
by Ihmori) means, however, that in experimenting at very low 

» J. Am. Chem. Soc. 42, 1402 (1920). 

61 Proc. Amsterdam Acad. 15, 445 (1912) . The abstract is quoted from Langmuir's paper. 
J. Am. Chem. Soc. 88, 2283 (1916). 

" Journ. Franklin Inst. 185. 29 (1918). 



156 Sorption of Gases at Low Pressures 

pressures special care must be taken to remove the water vapor 
by heating all parts to high temperatures with simultaneous 
absorption of the vapor in a liquid air trap or P2O5 tube. 

Gases and Vapors Evolved from Glass and Metals at Very Low Pressures 

While the study of sorption phenomena is of interest from 
the point of view of clean-up methods, the problem as to the 
nature and amounts of residual gases evolved in vacuum devices 
from the glass walls and metal parts is also of extreme import- 
ance in vacuum technique. 

The evolution of gas from the walls of bulbs such as are 
used for incandescent lamps has been investigated by I. Lang- 
muir. 53 "On heating bulbs of 40-watt lamps for three hours to a 
temperature of 200 deg. C, after having dried out the bulbs at 
room temperature for 24 hours by exposure in a good vacuum 
to a tube immersed in liquid air, the following average quantities 
of gas were given off: 

200 cu. mm. water vapor 
5 cu. mm. carbon dioxide 
2 cu. mm. nitrogen. 
"These are the quantities of gas, liberated by the heating, 
expressed in cubic millimeters at room temperature and atmos- 
pheric pressure. 

"By raising the temperature of the bulbs from 200 deg. to 
350 deg. C. an additional quantity of water vapor was obtained, 
so that the total now became 

300 cu. mm. water vapor 
20 cu. mm. carbon dioxide 

4 cu. mm. nitrogen. 

"A subsequent heating of the bulbs to 500 deg. C. caused the 
total amount of gas evolved to increase to 
450 cu. mm. water vapor 
30 cu. mm. carbon dioxide 

5 cu. mm. nitrogen. 

"At each temperature the gas stopped coming off the glass 
after a half hour of heating, only to begin again whenever the 
temperature was raised to a higher value than that to which the 
bulb had been previously heated. 

" It therefore seems that even by heating the bulb to 500 deg., 
not all of the water vapor can be removed, but it does seem prob- 
able that after this treatment the amount of water vapor that can 
come off a bulb at ordinary temperatures must be extremely small. 

« Trans. Am. Inst. Elec. Eng. 82, 1921 (1913), and J. Am. Chem. Soc. 88, 2283 (1916). 



Sorption of Gases at Low Pressures 157 

"The internal surface of this bulb was about 200 sq. cm. 
The number of molecules of gas given off per sq. cm. was thus 
56X10 15 molecules of H 2 0; 37X10 15 molecules of C0 2 , and 0.6 X 
10 15 molecules of N 2 . If we calculate the number of molecules 
of each of the gases necessary to cover a sq. cm. one molecule deep 
(taking the molecules to be cubical in shape) we find 1.0 X10 15 
for H 2 0; 0.77 X10 15 for C0 2 , and 0.67 X10 15 for N 2 . Thus the 
quantities of gas obtained from this bulb correspond to: a layer 
.of water do molecules deep, a layer of carbon dioxide 4.8 mole- 
cules deep and a layer of nitrogen 0.9 molecules deep." 

On the other hand, Langmuir has observed 54 that glass sur- 
faces previously heated to the softening point and then heated 
in vacuo gave off only 0.18 cu. mm. of water vapor (4.5 X10 15 
molecules) ; 0.032 cu. mm. of carbon dioxide (0.81 X 10 15 mole- 
cules) ; and 0.025 cu. mm. of nitrogen (0.63 X10 15 molecules). 
"These amounts correspond to the following number of layers 
of molecules: 4.5 for water vapor, 1.05 for carbon dioxide, and 
0.9 for nitrogen. It should be noted that the amounts of carbon 
dioxide and nitrogen correspond to unimolecular layers of these 
gases." 

Some very interesting experiments on determining the 
optimum conditions for evolution of water vapor from glass were 
carried out some time ago by Langmuir. It was observed that 
certain lamps made of sodium magnesium borosilicate glass 
(G-702-P) and consisting of high wattage filaments in very small 
bulbs blackened very rapidly if they were baked out at 550-600 
deg. C. during exhaust, while lamps baked out at 400-500 deg. 
G. did not blacken so rapidly. The effect was ascribed to water 
vapor evolved from the glass during the life of the lamp and 
experiments were therefore undertaken to try to remedy this 
condition. 

The following description of the experiments is taken from 
Langmuir's patent specifications. 55 

"Three lots of lamps were made with the same structural 
details and operating characteristics; the first lot was exhausted 
at approximately 450 deg. C, the second lot at 550 deg. C, and 
the third lot at 550 deg. C, at first and then at 400 deg. C. The 
average life of the first lot was approximately 575 hours, of the 
second lot 300 hours, and of the third lot over 900 hours, the con- 
ditions of operation with all three lots being the same." 

The explanation given of this result is as follows: "Appar- 
ently the treatment at 400 to 500 deg. C. liberates the water 

*< J. Am. Chem. Soc. 40. 1387 (1918). 
" Patent No. 1. 273. 629. July 23. 1918. 



168 



Sorption of Gases at Low Pressures 



vapor only from a comparatively thin surface layer of the glass. 
If, however, the exhaust is continued at 400 to 500 deg. C, no 
more water vapor will be drawn out of the deeper layers, and that 
which remains in the surface layer will be liberated." 



30 

\n 

< ,5 
10 
5 











i 






G-7 


K-P 


S/oss 


























If 


















X^ 


/ 








J/ 




^k 




*<r 




^S 


V* 


T""" 





100 200 300 400 500 600 
Deqrees-C. 

Fig. 62. Evolution of Gas from 
Corning G-702-P Glass 



The main conclusion arrived at by Langmuir is that in order 
to remove water vapor efficiently from the walls of glass vessels, 
the heating during exhaust should be carried out in two or more 
stages of gradually decreasing temperatures. He finds that one 
half-hour treatment at each of the above temperature ranges is 



€0 

50 

10 








1 






791 






~Sodt 


) Glass 












Cur/e 
" 


iTotal 












a 


ICO? 
4 Gas 




A 














n 





































100 ZOO 300 400 500 €00 
Degrees C. 

Fig. 63. Evolution of Gas from 
Soda Glass 



Sorption of Gases at Low Pressures 



159 



sufficient, and makes the interesting observation, which is in 
accord with that made by Sherwood (see below), that while the 
gas evolution at temperatures below 500 deg. C. practically 
ceases at the end of one half hour, the evolution of water vapor 
at higher temperatures continues indefinitely no matter how iong 
the heating period. Apparently the glass actually suffers a 
chemical decomposition at higher temperatures. 

An extensive series of investigations on the gases and vapors 
evolved from glass has been carried out at the Westinghouse 
Research Laboratory by R. G. Sherwood 56 and J. E. Shrader. 67 



30 
25 

JO 



^.15 



10 

5 












. 






Lead 


Glass 




1 












' 
















c* 


fa? 






1 


<_S 


{/ 




i 


jgk- 


k 




* 


*£ 



100 200 300 400 500 600 
Degrees C. 

Fig. 64. Evolution of Gas from 
Ordinary Lead Glass 



~ Sherwood measured the amounts of water vapor, carbon 
dioxide, and gases non-condensible in liquid air, liberated from 
different kinds of glass at various temperatures. Fig. 62 shows 
the results obtained with Corning G-702-P glass. This is a high 
melting-point glass which is used extensively in the manufacture 
of the gas-filled type of incandescent lamp. The samples of glass 
used in these measurements had a total area of about 350 sq. cm., 
and the curves show the amounts of gas liberated at different 
temperatures. The period of heating at each temperature was 
three hours. Figs. 63 and 64 show similar data with samples of 
soda glass, and lead glass respectively. It will be observed that 
in all cases the gas evolution first reaches a maximum which is 
at about 300 deg. C. for G-702-P, 150 deg. C. for soda glass, and 



fe 



Am. Chem. Soc. 40, 1645 (1918). 
>hys. Rev. IS, 448 (1918). 
•' Phys. Rev. IS, 434 (1919). 

See also abstract of a paper by Ulrey, Phys. Rev. 14, 160 (1919), which discusses the 
same subject. 



160 Sorption of Gases at Low Pressures 

200 deg. C. for lead glass, then decreases, and again rises rapidly 
at a temperature which is above the softening point of the glass. 
Sherwood concludes that the products removed below 300 deg. C. 
are adsorbed gases, while at higher temperatures there is an 
actual decomposition of the glass itself. In other experiments, it 
was observed that at the higher temperatures the gas evolution 
continued even after the samples were heated for 24 hours and 
longer. By previously annealing the glass at very high tem- 
peratures, the subsequent gas evolution in vacuo was decreased 
considerably, a result which is in accord with certain observations 
made by Langmuir and mentioned before. Similar results have 
been obtained in this laboratory by Mrs. M. Andrews and J. 
Pangburn in investigating the gases evolved from lamp bulbs. 
Analysing Sherwood's data, we find that, for instance, in the 
case of soda glass, the total gas evolved up to 200 deg. C. was 
about 50 cu. mm., or about 0.15 cu. mm. per cm. 2 , most of which 
was H 2 0; this would correspond to a layer of gas about four 
molecules deep. Sherwood concludes that the gases which are 
removed fairly rapidly at lower temperature are genuine ad- 
sorption products, as they correspond to quantities which are 
represented by a layer of gas which does not exceed one or tw^ 
molecules in thickness. As the temperature of the glass is raised 
to the softening point, the gas evolved consists practically wholly 
of H 2 and undoubtedly this arises, as mentioned above, from 
the chemical decomposition of the glass. 

Investigations by C. A. Kidner and H. A. Huthsteiner in 
this laboratory, on the rate of evolution of water-vapor and non- 
condensible gases from glass bulbs have shown that at the highest 
temperatures at which the exhausted bulb can be heated most of 
the adsorbed gas is evolved in the first two or three minutes. 
Preheating in dry air is also beneficial in removing most of this 
adsorbed gas. The pre-heating at ordinary pressure possesses 
the advantage that the glass can be heated to much higher 
temperatures, as there is no danger of the bulb's sucking inward. 

Some interesting measurements were carried out by Sher- 
wood on the adsorption of water vapor and other gases by dry 
surfaces of glass. Dry air could be removed very rapidly at 
ordinary temperature, while in the case of either moist air or air 
mixed with C0 2 , the rate of leakage at ordinary temperature was 
very slow. However, on heating to a high temperature prac- 
tically all this adsorbed gas could be removed in a few minutes. 
It is interesting to observe that in one experiment, after a pres- 
sure of about 10~ 4 mm. H 2 had been reached by exhausting, 
the bulb (of about 9000 cm. 3 capacity) was sealed off and after 



Sorption of Gases at Low Pressures 



161 



standing ten hours the pressure rose to 0.0095 mm. owing to the 
gas leakage from the walls, but did not materially increase sub- 
sequently. This gas could not be condensed in liquid air, thus 
showing that it was adsorbed air. The writer's experience has 
shown that invariably there is a slight increase in pressure after 
sealing off the pump. Part of this increase is due to gases ad- 
sorbed on the glass near the constriction which is heated to a high 



30 



I 

r 



-— £- 


V 


~--|- 


_=£! 


zz-z-tzfz 


«g^-== 



100 ZOO 300 4.00 
Deqrecs, C. 



500 



Fig. 65. Increase in Pressure in 
Sealed Bulb After Re-heating 



temperature during sealing off , and a portion is due to gradual 
leakage from the walls. Even with the utmost precaution in 
baking out at high temperature and low exhaust pressure, there 
is always a slight increase in pressure in the sealed-off device. 

In an investigation on the minimum pressure attainable 
with a Gaede rotary pump, S. Dushman observed 58 that unless 
care was taken to heat up the tubing connecting the gauge to the 
pump it was impossible to get below about 0.033 bars, because 
of the slow evolution of water vapor at ordinary temperature. 
When, however, the tubing was baked out at 330 deg. C, the 
pressure could be reduced to 0.0007 bars. Similar results have 
been reported by Shrader. The volume of the system exhausted 
in his experiments was about 2 liters. The effect of heat treat- 
ment on the vacuum obtainable after pumping until equilibrium 



Phys. Rev. 5, 212 (1915). 



162 



Sorption of Gases at Low Pressures 



was reached at that temperature is shown by the following 

results: 

Temperature 

20 100 200 300 500 
Press, in mm. 

1X10" 6 1.9 X10" 8 1.7 X10" 7 1.2 X10" 7 2.4 X10" 8 

Shrader also observed that not only does the vacuum in 
sealed vessels gradually deteriorate with time, at first rapidly 
and then more slowly, but also that "subsequent heating even 
at temperatures lower than the heat-treating temperature (on 
the pump) results in increase of pressure due to further libera- 
tion of gases and vapors from the glass." Fig. 65 shows the 
effect of heating a sealed-off system consisting of a 1500 cm. 3 
bulb and gauge of 500 cm. 3 capacity for one hour at increasing 
successive temperatures. In each case the bulbs had previously 
been heated at 500 deg. C. on the pump. 

E. W. Washburn, F. F. Footitt and E. N. Bunting 59 have 
published some data on the amounts of different gases obtained 
from glass when molten in vacuo. Table XXVII shows the 
results obtained with four different glasses : 

TABLE XXVII 
AMOUNT OF DISSOLVED GASES IN FINISHED GLASS 



Glass 


WEIGHT PER CENT 


VOLUME IN CM 3 PER 100 GM. AT 
NORMAL TEMP. AND PRESS. 




Ol 


C0 2 


N-2 


Total 


2 


CO, 


N-2 


Total 


Barium flint 1 . . . . 
Barium flint 2. . . . 

Light flint 

Borosilicate 


0.035 
.015 
.0045 
.0036 


0.011 
.0045 
.014 
.0035 


0.0025 
.0031 


0.046 
.020 
.21 
.010 


24.5 

10.5 

3.2 

2.5 


8.8 

3.6 

11.2 

2.8 


2.0 
2.5 


33.3 
14.1 
16.4 

7.8 


Water at deg. 
Cent 










5.15 


179.2 


2.24 





The last four columns give the volumes in cm. 3 at deg. 
C. and 760 mm. pressure, per 100 gm. glass. The solubilities 
in water at deg. C. are given for comparison at the bottom of 
the table. It is evident that the amounts of gases dissolved in 
molten glass are considerable. Compared with the volumes of 
gases actually evolved from glass vessels in high vacuum exhaust, 
even at the highest temperatures practicable, the volumes ob- 
served for molten glass are much larger. This probably accounts 
to some extent for the observed increases in pressure in sealed-off 
glass vessels. 

s»Univ. of Illinois Bulletin No. 118. Dissolved Gases in Glass, Dec, 1920. 



Sorption of Gases at Low Pressures 163 

With regard to gases evolved from metals heated in vacuo, 
the prevailing opinion has been that very large quantities are 
evolved. It has been shown, however, by Langmuir 60 that when 
care is taken to remove water vapor and carbon dioxide from the 
glass walls, the amount of gas actually liberated from a tungsten 
filament is not more than three to ten times the volume of the wire. 
Most of the gas is eliminated by heating the wire to 1500 deg. C. 
It consists of about 70 to 80 per cent CO, the remainder being 
mostly H 2 and C0 2 . "The total amount of gas evolved from the 
filament of a 40- watt lamp, if liberated in the lamp after sealing 
off, would produce a pressure of from 0.006 to 0.02 mm." Lang- 
muir has also observed that the total volume of hydrogen and 
carbon monoxide obtained from a platinum wire heated to 350 
deg. C. is only about one-tenth of the volume of the platinum. 

The following data on the amounts and composition of gases 
evolved from different metals heated in vacuo were obtained 
by Mr. S. P. Sweetser of this laboratory. The experi- 
mental method used was that developed by Langmuir for 
the above mentioned measurements on tungsten and platinum. 
The metal in the form of a filament about 0.05 to 0.06 cm. diam- 
eter and 15 cm. long was heated to a bright red heat, and the 
heating continued until the rate of evolution of gas had decreased 
to a very low value. 

Different samples of "untreated" nickel wire gave off 
amounts of gas varying from 5 to 15 cu. mm. of gas, consisting 
of about 75 to 90 per cent CO, and 20 to 10 per cent C0 2 , with 
small amounts of H 2 . 

Similarly wires of monel metal, copper, and copper coated 
nickel-iron wire ("dumet" wire used in making lead-in- wires in 
lime-glass and lead-glass incandescent lamp bulbs) gave amounts 
of gas varying from 3 to 20 cu. mm. of gas. The composition of 
the gas was approximately the same as that evolved from the 
nickel wires. 

An investigation of the composition of the gas evolved from 
the copper anodes used in the radiator-type of Coolidge X-ray 
tube gave the following average results: 

C0 2 7 per cent 

CO 92 per cent 

Nj-f-Hz 1 per cent 

It will be observed that in the experiments with wires, the 
total volume of metal used was about 0.03 cm. 3 or 30 cu. mm., 
and only in exceptional cases did the volume of gas evolved on 
heating the metal exceed the volume of the filament. 

«° Trans. Am. Inst. Elect. Eng. 32, 1921 (1913). See also Journ. Am. Chem. Soc. So. 105 
(1912) for method of analysis. 



164- Sorption of Gases at Low Pressures 

Lead-in wires and supports which cannot be heated by- 
passing current through them or by electronic bombardment 
(in the case of hot cathode devices) gradually evolve gases which 
cause progressive deterioration of the vacuum in sealed-off 
vessels, so that it is necessary in such cases either to give all the 
metal parts that can be heated during the exhaust a much more 
severe heating than they will be subjected to subsequently, and 
thus heat the other parts by radiation or else to provide some 
substance which will clean up residual gases during life. 

From the above data it is evident that the gases gradually 
evolved from imperfectly evacuated metal parts must cause 
fairly appreciable changes in pressure in sealed-off vessels. Thus, 
let us consider a 3000 cm. 3 (7-inch diameter) bulb exhausted to a 
pressure of 0.01 bar. If this bulb contains a metal filament of 
the size used in the above determinations (a not unusual case), 
which has not been heated on the pump, the amount of gas 
evolved on subsequent heating, assuming it to be 10 cu. mm., 
will increase the pressure in the bulb to about 3.4 bars. Such a 
pressure would absolutely ruin the device for any electron 
emission phenomena, and in order to keep the pressure below 
0.1 bar, the residual gas in the filament would have to be less than 
0.3 cu. mm. ; that is, over 97 per cent of the total gas contained 
in the filament would have to be eliminated on the pump. 

A modification of Langmuir's method of analysis of small 
quantities of gas has also been described more recently in detail 
by H. M. Ryder. 61 The latter has determined by this method 
the composition of the gases eliminated from untreated com- 
mercial copper heated in vacuo. 62 The gases evolved, in order 
of decreasing amounts, were C0 2 , CO, H 2 and N 2 . The total 
volume from a sample weighing 5 gm. and having a volume of 
1.31 cm. 3 was over 200 cu. mm. On heating to 750 deg. C. and 
higher, large amounts of 2 were evolved, probably due to decom- 
position of Cu 2 contained in the copper. Here also, the volume 
of gas evolved was much less than that of the metal. 



«i J. Am. Chem. Soc. 40. 1656 (1918). N. R. Campbell (Proc. Phys. Soc. 83, 287, 1921) 
has developed a method for the micro-analysis of gases which is based on the differences in 
condensation temperature of the various gases, and in which use is made of a Pirani-Hale 
gauge. 

«2 J. Franklin Inst. 187, 508 (1919). 






165 



CHAPTER V 

CHEMICAL AND ELECTROCHEMICAL 
CLEAN-UP OF GASES AT LOW PRESSURES 



CHEMICAL METHODS FOR THE CLEAN-UP 
OF RESIDUAL GASES 

As has been mentioned in the previous chapter, it is often 
extremely difficult to draw any distinct line of demarkation 
between so-called purely physical and purely chemical reactions 
when dealing with clean-up processes at low pressures. In the 
general discussion of sorption phenomena it has been necessary 
to refer to reactions which are undoubtedly chemical inasmuch 
as definite compounds are formed. Thus, when hydrogen is 
taken up by the alkali metals, we have every evidence that a 
chemical compound, a hydride, is formed. On the other hand, 
it is still a debatable question as to whether a hydride is formed 
in the reaction between hydrogen and palladium. 

In this chapter we shall discuss a type of clean-up reaction 
in which the gas disappears because of a reaction with a 
heated solid. The resulting compounds are volatile at the tem- 
perature of the reaction and condense on colder parts of the 
system, thus making it possible for the clean-up to continue as 
long as residual gas is present. On the other hand, since the rate 
of clean-up decreases ordinarily with the pressure, a point is 
reached at which the rate of disappearance of gas is equal to the 
rate of evolution from walls and other parts of the system. 

Clean-up of Gases by Calcium 

The use of this method for the production of high vacua 
was first proposed by F. Soddy. 1 He found that in a gas at 
reasonably low pressure, the heating of calcium to a temperature 
at which it begins to volatilize would cause the pressure to de- 
crease rapidly to a point at which the gas is "non-conducting." 
For heating the calcium, Soddy recommends either a small 
quartz-tube furnace wound with platinum wire, or an inductive 
method of heating (analogous to that used in the most recent 
types of high-frequency furnaces devised by Northrup). No data 
are given by Soddy as to the degree of vacuum actually attained 
or to the rate of clean-up. As an indicator of the degree of 
vacuum, he used a spectrum tube and described his results as 
follows : 



Proc. Roy. Soc. London, 7S, 429 (1907). 



166 Chemical and Electrochemical Clean-up of Gases at Low Pressures 

"If the apparatus (consisting of a large vessel in which is 
contained the quartz-tube furnace), charged with a small piece 
of calcium, and furnished with a Plucker spectrum tube, is 
exhausted by a Fleuss pump and the furnace heated, gases 
consisting of compounds of hydrogen, carbon, and oxygen are 
given out by the calcium. If the connection with the pump is 
then shut off and the heating continued, absorption of the 
remaining gases accompanied by volatilization of the calcium 
takes place, and the vacuum rises almost instantly to a point 
at which no discharge can be passed through the spectrum tube. 
By a non-conducting vacuum is to be understood one of greater 
resistance than an alternative spark-gap in air of 2 to 3 cm." 

Soddy observes that CO, C0 2 , H 2 0, C 2 N 2 , S0 2 , NH 3 , and 
oxides of nitrogen are all readily cleaned up. In the case of 
hydrogen the absorption is not so great. "There is no doubt," 
he states, "that a low initial pressure, not exceeding a few 
millimeters of mercury, is as essential a condition in causing 
calcium to combine with gases as a high temperature. For rapid 
and continuous absorption, volatilization is essential. The film 
of volatilized metal continues, even in the cold, to absorb, 
although more slowly than the vapor itself." 

Argon, helium and the other rare gases are, of course, not 
cleaned up by calcium, so that this method has proved useful 
for the purification of the rare gases. J. H. Clough, 2 of this 
laboratory, found that for this purpose the best results are 
obtained by means of a discharge tube containing a solid calcium 
anode and robust tungsten filament as cathode. The two elec- 
trodes are placed fairly close to each other, and on lighting the 
filament it is possible to start an arc in the rare gases at very low 
voltages. Under the action of the arc, the calcium at the anode 
is gradually volatilized and the chemically active gases are 
absorbed. 

Clough also observed that titanium and magnesium are very 
effective as clean-up metals when used in the above manner. 
There is some evidence according to G. M. J. Mackay 3 that the 
reaction here is not altogether a straight chemical one. "Appar- 
ently the arc activates the gaseous impurities so that they 
combine more readily with the chemical agents (calcium, etc.), 
in the bulb." 

In order to obtain some data on the practical value of the 
calcium reaction in cleaning up residual gases, C. A. Kidner and 
S. Dushman carried out some experiments with hydrogen. This 

» Patent Specification No. 1,246,054 (1917). 
» Patent Specification No. 1,208,597 (1917). 



Chemical and Electrochemical Clean-up of Gases at Low Pressures 167 

gas was chosen because it is the most difficult to clean up, and 
also because it is the most frequent constituent of residual gases 
present in high vacuum devices. 

Calcium in the form of wire was laid inside a tungsten spiral, 
so that it could be heated by passing current through the latter. 
By varying the filament current, the rate of volatilization could 
be varied and the rate of clean-up measured under different 
conditions. The pressure was measured by a McLeod gauge, 
and the volume of the system containing hydrogen was 2500 
cm 3 . In one experiment, the pressure was decreased from 250 
to 4 bars (approximately) in almost 30 minutes. At the end of 
this interval the calcium had been practically all volatilized and 
covered the sides of the bulb. It was observed that the rate of 
clean-up increases with the temperature of the calcium and is 
apparently proportional to the pressure of hydrogen. 

Similar experiments were tried with magnesium, but no 
noticeable clean-up was observed. Soddy found that strontium 
and barium act similarly to calcium, but as the latter can now 
be obtained commercially in very pure form it is much more 
convenient for use. Soddy also observed that the presence of 
CaH 2 in the calcium makes the metal much more difficult to 
volatilize. 

Measurements by Kidner at higher pressures (10 to 100 
bars) showed that the calcium deposit on the glass does not 
adsorb either hydrogen or oxygen to any marked extent. Even 
active hydrogen (formed by heating a tungsten filament to a 
high temperature in the hydrogen) is only slightly adsorbed by 
the cold calcium deposit. On the other hand, in some earlier 
experiments in which an ionization gauge was used, it was ob- 
served that with a low initial pressure of hydrogen the calcium 
deposit does clean-up the gas gradually. Thus, in one case, the 
pressure in a sealed off system of about 500 cm 3 capacity de- 
creased from 2 to 0.7 bars during the volatilization of the calcium 
(which occurred in a few minutes) , and subsequently the deposit 
continued to adsorb gas until at the end of two hours the pressure 
had decreased to about 0.0007 bars. 

These observations, along with Soddy' s results, lead to the 
conclusion that, in order to clean-up large amounts of gas with 
calcium, it is necessary to heat the metal to a high enough tem- 
perature to cause fairly rapid volatilization. On the other hand, 
with calcium volatilized in a low pressure of gas so that the 
deposited metal is presumably not saturated with gas, the cold 
deposit gradually adsorbs the small amount of residual gas and 
it is thus possible to obtain a fairly low pressure. In using 



168 Chemical and Electrochemical Clean-up of Gases at Low Pressures 

calcium to clean-up small traces of residual gas, it is naturally 
advisable to heat the metal for a short interval of time while 
the system is still connected to the exhaust pump, to get rid of 
occluded gases. 

Clean-up of Residual Gases by Incandescent Tungsten Filaments 

In a series of investigations on the reactions between dif- 
ferent gases and heated tungsten filaments, I. Langmuir ob- 
served that under certain conditions a chemical clean-up of the 
gas occurs. 4 The principal gases studied were oxygen, nitrogen, 
hydrogen, carbon monoxide and dioxide, chlorine, bromine and 
iodine, methane, cyanogen, hydrochloric acid, argon, phosphine, 
and the vapors of many substances, such as mercury, phosphorus 
pent oxide, sulphur, etc. While the discussion of the theoretical 
aspects of these investigations must be reserved for a subsequent 
section, we shall mention briefly, in the present connection, the 
conditions under which the best clean-up results can be obtained 
with different gases. 

(1) Clean-up of Oxygen by a Tungsten Filament 5 

At temperatures above 1200 deg. K., and at pressures below 
about 100 bars, the oxide W0 3 "distills off as fast as it is formed, 
leaving the surface clean and bright." The rate of decrease of 
pressure (at constant filament temperature) is proportional to 
the pressure at any instant, that is, the reaction is of the first 
order. If p denotes the original pressure, the pressure p at any 
interval of time t, after the beginning of the experiment, is given 
by the relation, 

or 

p = p ot -ktA/v (52) 

where k is a constant whose value depends on the temperature 
of the filament, V denotes the volume of the system, and A the 
area of the filament. Furthermore as k increases exponentially 
with the temperature, it follows that to obtain a rapid clean-up 
the temperature of the filament should be made as high as prac- 
ticable (ordinarily about 2500 to 2700 deg. K.). 

In a typical experiment in which the volume of the system 
used was 1075 cm 3 , and the initial pressure 9.41 bars (7.06 X10 -3 
mm. of mercury), a tungsten filament 5.4 cm. long and 0.0394 

< Dr. Langmuir has reviewed the results of these investigations up to 1915 in a paper 
on "Chemical Reactions at Low Pressures," J. Am. Chem. Soc. 87, (1915); also see J. 
Industrial and Eng. Chem.. /. 348 (1915). 

5 J. Am. Chem. Soc. So, 105 (1913). 



Chemical and Electrochemical Clean-up of Gases at Low Pressures 169 



mm. diameter was heated to 1470 deg. K., and it was observed 
that the pressure decreased to one per cent of its initial value 
in 23.5 minutes. The initial amount of oxygen, measured at 
298 deg. K. and atmospheric pressure was 10 cubic mm. Fig. 66 
shows the quantity of oxygen present at any instant plotted 



iao - 




































oo 5 






































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10 1 


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V s 


































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8 18 

IB 


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9 


2 





2 


4 


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Time (Minutes) 

Fig. 66. Rate of Disappearance of Oxygen in Presence of Incandescent 
Tungsten Filament at Different Temperatures 

(on semi-logarithmic paper) as ordinate against the time^ in 
minutes. From the form of equation (52) it is evident that,jfor 
equal intervals of time, the pressure must decrease in the same 
ratio, so that plotted on semi-logarithmic paper the resulting 
graph is a straight line. From this curve and the measurements 
on the variation in k with temperature, the graphs for a number 



170 Chemical and Electrochemical Clean-up of Gases at Low Pressures 



of other temperatures have been calculated and drawn in. The 
table which follows gives the value of the interval of time that 
would be required to reduce the total quantity of oxygen to 0.1 
per cent of its original value if the tungsten filament described 
were heated to different temperatures. 





T 


t 




(degrees absolute) 


(minutes) 




1470 


34.5 




1570 


19.5 




1770 


7.2 




2020 


3.7 




2290 


1.93 




2520 


1.52 




2770 


1.22 



At pressures below about 0.001 bar there is evidence that 
oxygen does not perceptibly attack a tungsten filament, so that 
this would appear to be about the lower limit of pressure attain- 
able with this method. 

(2) Clean-up of Nitrogen by a Tungsten Filament 6 

At pressures below about 100 bars, the rate of clean-up of 
nitrogen by a tungsten filament maintained at constant tem- 
perature is observed to be constant down to pressures as low as 
about two or three bars. It has been shown by Langmuir that 
the clean-up is due to combination between tungsten atoms 
evaporated from the filament and nitrogen molecules to form 
WN 2 . Hence, in the foregoing range of pressures, the rate of 
clean-up is governed exclusively by the rate of evaporation of 
tungsten and increases with the latter. Fig. 67, taken from 
Langmuir's paper, gives the rate of clean-up in cubic mm. of 
nitrogen (measured at 298 deg. K. and atmospheric pressure) 
per minute per sq. cm. of tungsten filament, as a function of the 
temperature. " At lower pressures the rate is no longer constant 
because the nitrogen molecules become so scarce that a large 
fraction of the tungsten atoms strike the bulb without colliding 
with nitrogen molecules." However, on cooling the bulb con- 
taining the filament in liquid air, the tungsten atoms are found to 
combine with the nitrogen molecules adsorbed on the glass, and 
the rate of clean-up is materially increased. As will be described 
more fully in another section this observation has been applied by 
Langmuir in obtaining extremely high vacua. 

• J. Am. Chem. Soc. 85, 931 (1913). 
Z. Anorg. Chem. 85, 261 (1914). 



Chemical and Electrochemical Clean-up of Gases at Low Pressures 111 

(3) Clean-up of Carbon Monoxide by a Tungsten Filament 7 

"With the bulb at room temperature, carbon monoxide was 
observed to behave exactly like nitrogen. In fact, with the 
filament at a given temperature, the curves obtained first with 
nitrogen and then with carbon monoxide proved to be identical. 



0)5.0 

L. 
<D 

3 



4.0 



3.0 



2.0 



10 



2400 























































































































































































































1 
































r 
































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o 


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y 








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-^1 

































2500 2600 2700 

Temperature (Helv/n) 



2800 



Fig. 67. Rate of Disappearance of Nitrogen in Presence of 
Incandescent Tungsten Filament 



This proved that each atom of tungsten combined with one mole- 
cule of CO, presumably to form a compound WCO." With the 
bulb immersed in liquid air, the rate of clean-up was observed 
to be very much greater, but still linear, as in the case of nitrogen 
and CO at ordinary temperatures of the bulb. 



J. Am. Chem. Soc. 37, 1159 (1915). 



172 Chemical and Electrochemical Clean-up of Gases at Low Pressures 

(4) Clean-up of Hydrogen by a Tungsten Filament 8 

When a tungsten wire is heated to a temperature above 
1300 deg. K. in hydrogen at low pressure (1 to 20 bars), a portion 
of the gas is dissociated into atomic hydrogen and this is readily 
adsorbed by glass surfaces at room temperatures and much more 
at liquid air temperatures. It is possible in this manner to clean- 
up 20 to 50 cubic mm. of hydrogen. 9 A limit to this clean-up is, 
however, set by the fact that the ' ' hydrogen atoms react to form 
molecular hydrogen as soon as they come in contact, even at 
liquid air temperatures." The amount of hydrogen gas that can 
be cleaned up in this manner by a heated tungsten filament is 
very variable and fatigue effects are apt to be observed, so that 
this method cannot be recommended as very useful in cleaning 
up residual amounts of hydrogen gas. 

Traces of oxides present in a bulb are reduced by the active 
hydrogen with formation of H 2 0. The latter is then dissociated 
again at the filament forming WO3 (which distills to the bulb) 
and active hydrogen, which again reacts with the WO 3 on the 
bulb to form tungsten and H 2 0. The result is that the glass 
walls become covered very rapidly with a black deposit, due to 
the disintegration of the filament. This is also the reason that 
even slight traces of water vapor in the presence of a heated 
tungsten filament will produce an apparently continuous evolu- 
tion of gas. 10 

(5) Vacuum Attainable by Heating a Tungsten Filament in Con- 

tact with Residual Gases 
The observation that a tungsten filament heated to a very 
high temperature causes the clean-up of practically every gas to 
a very low pressure was utilized by Langmuir in the production 
of the extremely high vacua that are necessary for obtaining 
accurate data on the electron emission of metals. - 1 The method 
used is as follows : The bulb into which the electrodes are sealed 
also contains an auxiliary tungsten filament. After evacuating 
and heating all the metal parts to a high temperature while on 
the pump, the bulb is sealed off, immersed in liquid air, and the 
auxiliary filament heated to 2800 to 2900 deg. K. 12 The residual 
gases are cleaned up to a very low pressure and if the bulb is kept 
immersed in liquid air while making the electrical measurements, 
this high vacuum is maintained. 

s See references in J. Am. Chem. Soc. 37, 1161 (1915). 

•Trans. A.I.E.E. 82, 1913 (1913). 

10 This effect has been described bv Langmuir more fully in the above paper. 
» Zeits. f. Elektrochem. 15, 516 (1914). 

12 For method of determining the temperature of tungsten filamants, see I. Langmuir, 
General Electric Review, 1.9, 208 (1916). 



Chemical and Electrochemical Clean-up of Gases at Low Pressures 178 

Some experiments made at the writer's suggestion by Messrs. 
H. Huthsteiner and C. A. Kidner to determine the degree of 
vacuum attainable by this method yielded interesting results. 
Using a hairpin filament about 0.0076 cm. diameter and 7.5 cm. 
long, with heavy nickel leads (0.1 cm. diameter) to prevent 
excessive heating of the latter, it was possible by heating the 
filament to 2700 deg. K. to obtain a clean-up from about 0.02 
bar to 0.0015 bar, the pressure being measured by an ionization 
gauge attached to the bulb. An appendix sealed onto the sys- 
tem, consisting of the gauge and bulb, was then immersed in 
liquid air and on heating the filament to 2700 deg. K. the pressure 
was observed to decrease to 0.001 bar. 

In another experiment in which the bulb containing the 
tungsten filament was wholly immersed in liquid air during 
evaporation of the tungsten, the pressure was decreased from 
about 0.1 bar to 0.005 bar. Taking into account the fact that 
during these experiments the ionization gauge itself was not 
immersed in liquid air, there is no doubt that the degree of 
vacuum attainable in Langmuir's experiments must have been 
better than 0.0005 bar, and probably nearer 0.0001 bar. 

In some more recent experiments, Huthsteiner has observed 
that a small trace of P 2 5 , sublimed into the bulb before sealing 
it off the pump, materially assists, in the presence of the heated 
filament, in cleaning up residual gases to a very low pressure. 
This is evidently due to the fact, previously observed by G. M. J. 
Mackay, 13 that P2O5 is capable of cleaning up very large amounts 
of atomic hydrogen. Also the well-known hygroscopic properties 
of P2O5 make it a very efficient reagent for absorbing residual 
water-vapor. The only disadvantage of this substance is its 
comparatively high vapor pressure even at ordinary temperature. 
It has, however, been observed in this laboratory that fused 
P 2 5 has a lower vapor pressure. 

Some experiments carried out a number of years ago by 
Mackay and Huthsteiner yielded interesting results on the 
quantities of hydrogen and nitrogen that can be cleaned up by 
P 2 5 in the presence of a heated tungsten filament. By heating 
the filament to 2300 deg. K., the pressure in a volume of 850 
cm 3 could be reduced from 150X10~ 3 mm. to 1X10 -3 mm. of 
mercury in two minutes. With the filament at 2700 deg. K., the 
pressure was reduced from 1.005 mm. to 4X10 -3 mm. in about 
three minutes. That the clean-up is due to P 2 5 vapor was 
shown by cooling the bulb to the temperature of liquid air, 
when there was observed only a slight disappearance of hydrogen. 

« See Patent Specification No. 1,249.978 (1917), and also Xo. 1,208,597 (1917). 



774 Chemical and Electrochemical Clean-up of Gases at Low Pressures 

ELECTRICAL CLEAN-UP OF GASES AT HIGHER PRESSURES 

The gradual clean-up of gas during the passage of an elec- 
trical discharge in a "vacuum" tube was first observed by 
Pliicker in 1858. As the gas disappears, the voltage required 
to pass current through the tube increases and, finally, the 
vacuum becomes "non-conducting." In the gas-filled X-ray 
tube, this phenomenon was known as "hardening," since the 
higher the voltage required to produce the discharge, the 
"harder" the resultant X-rays became. 14 In spite of the large 
number of investigations on this subject, the exact cause of the 
phenomenon is as yet an open question. "The effect is undoubt- 
edly not a simple one, and there are probably several contribu- 
tory causes." S. Brodetsky and B. Hodgson 15 have given the 
following list of the explanations which have been proposed : 

(1) Chemical action between the gas and the glass 16 

(2) Chemical action between the gas and the cathode 17 

(3) Chemical or mechanical action between the gas and 
the anode 18 19 20 

(4) Chemical action due to active nitrogen 21 

(5) Mechanical occlusion of the gas in the glass 22 

(6) Mechanical occlusion of the gas in the cathode 23 

(7) Mechanical occlusion of the gas in the disintegrated 
part of the cathode. 24 

It is well to remember in this connection that, according 
to our present views, electric conduction in gases occurs by 
means of electrons and positive ions, the latter being produced 
either by bombardment of the anode by electrons or by collision 
of the latter with gas molecules. The positive ions attain, under 
even moderate voltages, velocities which are much greater than 
those possessed by ordinary gas molecules in virtue of their 
kinetic energy of translational velocity. Thus, at ordinary 
temperature, the mean velocity of a molecule of hydrogen is 
about 1900 meters per second, and that of a molecule of nitrogen 

14 See, for instance, G. W. C. Kaye, "X-Rays," which gives in Chapter VI, a discussion 
of this effect as observed in the older type of X-ray tubes. 
»s Phil. Mag. 31, 478 (1916). 
" R. S. Willows, Phil. Mag. 6, 503 (1901). 
» Mey, Ann. d. Phvs., 11, 127 (1903). 
i» C. A. Skinner, Phil. Mag. 12, 481 (1906). 
i» B. Hodgson, Phys. Zeits. 13, 595 (1912). 

20 V. L. Chrisler, Phys. Zeits. 10, 745 (1909); Phys. Rev. 29, 461 (1909). 
2i S. E. Hill, Proc. Phys. Soc. London, 25, 35 (1912). 

22 Campbell-Swinton, Proc. Roy. Soc. 79, A, 134 (1907). 

23 Riecke, Ann. d. Phys. 15, 1003 (1904). 

2« F. Soddy and Mackenzie, Proc. Roy. Soc. 80, A, 92 (1908). 



ERRATUM 

Page 175, lines 9 and 18 
For "100 volts" read "one volt" 



Chemical and Electrochemical Clean-up of Gases at Low Pressures 175 

about 500 meters per second. When these molecules are ionized, 
the velocity, u, is given by the relation 

y 2 mu 2 =Ve (50) 

which has been used already in Chapter III in connection with 
the theory of the ionization gauge. 

Converting to ordinary units, this relation becomes 

u = L396X10«Vv/M cm. sec- 1 . (50a) 

where V is expressed in volts and M is the molecular weight 
of the gas. Hence at 100 volts, the velocity of a hydrogen ion 
would be 9800 meters per second, and that of a nitrogen ion 2600 
meters per second. At higher voltages, the velocities would be 
still greater. It is therefore reasonable to expect that such high 
velocity molecules might be able to penetrate into the glass walls 
in much the same manner as the alpha particles (positively 
charged helium atoms) expelled by radioactive atoms. On the 
other hand, if we compare the energy of high velocity ions with 
the kinetic energy of molecules at higher temperatures, we find 
that a hydrogen ion moving through a field of 100 volts has the 
same kinetic energy as a hydrogen molecule at about 7500 to* 
8000 deg. K. It would therefore not surprise us to find that such 
ions are capable of combining chemically with molecules upon 
which they happen to impinge. 

According to Langmuir 25 both these types of reactions 
occur in the clean-up of nitrogen in presence of a hot tungsten 
cathode when an electric discharge passes. At higher pressures, 
the reaction is "electro-chemical," the nitrogen combining with 
the tungsten to form the nitride WN 2 . At very low pressures 
and high anode voltages, the action is apparently purely me- 
chanical (Langmuir designates this the "electrical" clean-up). 
The nitrogen is driven into the glass in such a form that it can 
be recovered by heating. The action is thus apparently re- 
versible, and only limited quantities of nitrogen can be cleaned 
up in this manner. The electric clean-up, as distinguished from 
the electro-chemical, also exhibits distinct fatigue effects. 

It is quite probable that both these two types of clean-up 
occur simultaneously in practically all the cases where gases 
disappear during electrical discharge, and we shall find that this 
point of view enables us to interpret to a large extent the many 
apparently contradictory results obtained by the different 
investigators. 

Willows 16 observed that the amount of clean-up of gas in a 
discharge tube varied according to the nature of the glass from 

» J. Am. Chem. Soc. 35, 931 (1913). 




176 Chemical and Electrochemical Clean-up of Gases at Low Pressures 



which the tube was made. The absorption was least in Jena 
glass, more in lead glass, and greatest in soda glass. At constant 
current, the amount of gas occluded was found to increase with 
decrease in pressure. The conclusion arrived at was that the 
clean-up is due to chemical reactions between the gases and the 
glass walls. In support of this view, S. E. Hills 21 has shown that 
absorption is observed with air in an electrodeless discharge. His 
experiments were carried out in the range of pressures varying 
from 0.4 mm. to 0.04 mm. of mercury. During these experi- 
ments the bulbs became covered with a dark deposit on the 
walls, presumably due to oxidation reactions. On exhausting 
these bulbs and filling them with hydrogen at about one mm. 
pressure, the discharge caused a rapid disappearance of the gas 
and the deposit became lighter colored, which Hills accounted 
for by chemical reduction. Willows has repeated Hills' experi- 
ments 26 with quartz vacuum tubes, and observes that "a new 
quartz bulb does not absorb air, but if it be fed with repeated 
doses of hydrogen — which are absorbed when an electrodeless 
discharge is passed — it then, becomes very active. If discharges 
in hydrogen are alternated with those in air the bulb can be 
made to absorb large quantities of either gas and the activity 
with each gradually increases." Willows accounts for these 
results by assuming, as Hills does, alternate oxidation and 
reduction. 

Mey 17 has shown that when potassium and sodium amalgams 
are used as electrodes, compounds of these metals with hydrogen 
and nitrogen are formed during the discharge, and G. Gehlhoff 27 
has utilized this observation to purify rare gases (Ar, He, Ne, 
etc.). In the presence of a glow discharge with a heated alkali 
metal as cathode, all the chemically active gases are removed 
from a mixture of these with the rare gases. Nitrogen is com- 
pletely absorbed even with the alkali metal at ordinary tem- 
peratures. In the case of hydrogen complete absorption occurs 
with sodium at 290 deg. C, and with potassium at 175 deg. C, 
while rubidium and caesium are effective at even lower tem- 
peratures. Gehlhoff believes that chemical combination occurs 
between the vapors of the metals and the residual gases in an 
active state. 

The absorption of hydrogen by sodium-potassium electrodes 
has also been investigated by R. C. Gowdy. 28 Absorption was 
observed to occur when the alloy was used as cathode, and 

26 Proc. Pfcys. Soc. London, 28, 124 (1916). 

« Verh. d. deutsch. physikal. Ges. IS, 271 (1911). 

28 Phys. Rev. 4, 401 (1914). 



Chemical and Electrochemical Clean-up of Gases at Low Pressures 177 

evolution when used as anode. The hydride is apparently de- 
composed by the cathode rays. 

The most recent work on this subject is that of F. H. 
Newman. 29 He deposited different elements in a pure condition 
on the cathode of an electric discharge tube and then determined 
the absorption of different gases on passing an electric discharge. 
The minimum pressure at which clean-up was observed to occur 
varied around 0.1 to 1 mm. of mercury. "Measurements were 
made to compare the amount of nitrogen gas absorbed by the 
element in the tube with the quantity of electricity passing in 
the circuit. Potassium, sodium, mercury, cadmium, antimony, 
magnesium, calcium, zinc, tin, phosphorus, sulphur, and iodine 
were tested in this way. The rates of absorption were very great 
with the last three elements. Hydrogen gas was also used in the 
tube, and absorption occurred with phosphorus, sulphur, and 
iodine." Newman concludes from his experiments that the 
clean-up is due to chemical reactions between the elements 
present on the cathode and the gases which assume active modi- 
fications on the passage of an electric discharge. 

In this connection it is interesting to refer briefly to the 
experiments carried out by R. J. Strutt 30 on the formation and 
properties of a chemically active modification of nitrogen. He 
observed that on passing a condenser discharge through nitrogen 
at low pressures, a form of nitrogen is obtained which show T s an 
intense yellow glow and is very active chemically. As well 
known, nitrogen in the ordinary state is very inert chemically. 
It combines with other elements with difficulty and only under 
special conditions such as high temperature or high pressure. 
On the other hand, Strutt finds that the nitrogen passed through 
the discharge tube under the above conditions is very active 
chemically. "Drawing it by the pump over a small pellet of 
phosphorus, a violent reaction occurs, red phosphorus is formed, 
and the yellow glow is quenched. At the same time the gas is 
absorbed." Similarly active nitrogen combines readily with 
iodine, sulphur, and arsenic. There is no doubt, therefore, that 
the formation of active nitrogen must be taken into account in 
explaining clean-up effects in electrical discharges. 

In a similar manner Newman accounts for the absorption 
of hydrogen by phosphorus, sulphur and iodine, by assuming 
the formation of an active modification of the gas. This is 
probably the same form as that produced by Wendt and Lan- 

*» Engineering, Jan. 14, 1921, p. 60. 

Proc. Phys. Soc. London, 32, 190 (1920); 33, 73 (1921). 
:,n Proc. Roy. Soc. 85, A, 219 (1911) and subsequent papers. 



178 Chemical and Electrochemical Clean-up of Gases at Low Pressures 

dauer 31 in subjecting hydrogen to a-rays from radium emanation 
or to high potential corona discharges. 

These observations and the results obtained by Langmuir 
on the electrochemical clean-up of nitrogen by a heated tungsten 
cathode indicate that the above theory probably accounts for 
some of the clean-up effects observed in discharge tubes. As 
pointed out by Kaye: " It may be, also, that the action is stimu- 
lated by a species of electrolysis of the glass produced by the 
high-tension discharge playing over its surface. It is well known 
that glass may be readily electrolyzed by quite moderate poten- 
tials if the temperature of the glass is raised ; and it is a matter of 
experience that the discharge seems to have an ageing effect on 
the glass, to the detriment of subsequent working on the blow- 
pipe. Such electrolysis might have a marked effect on the gas 
film which glass and other solids can condense on their surfaces." 

That, however, the clean-up occurs owing to reactions 
which are not chemical is shown by the fact, observed by Soddy 
and Mackenzie, 24 that both pure helium and neon are also 
absorbed in electric discharge tubes. With aluminum electrodes, 
such as were used in their experiments, the electric discharge 
causes a considerable mechanical disintegration of the cathode, 
and the portions of glass adjacent to this electrode become 
covered with a deposit of the metal in a finely divided state. 
This phenomenon is known as "cathodic sputtering" and occurs 
to a larger or smaller extent according to the composition of the 
cathode. 

From the fact that the gases could be recovered by heating 
the tubes, Soddy and Mackenzie concluded that the gases were 
mechanically adsorbed by the deposits formed around the 
cathode. The finely divided metal formed by sputtering is thus 
assumed to behave like palladium or platinum black in the 
ordinary adsorption phenomena. That cathodically sputtered 
metals adsorb hydrogen during discharge has been shown by 
Heald, 32 and other investigators. 

C. A. Skinner 33 found in his experiments that gas was evolved 
at the cathode and absorbed at the anode. The gas evolution 
occurred at a rate given by Faraday's law, that is, 1 gm. of 
hydrogen for 96,500 coulombs. It is to be noted that with fresh 
electrodes a number of observers have found that ' ' there is often 
an initial evolution of gas, especially in hydrogen and nitrogen, 
or in any gas, with aluminum electrodes. But if the tube is used 

" T. Am. Chem. Soc. 4* (1920). 

» Phys. Rev. 24, 269 (1907). 

" Phil. Mag. 12, 481 (1906); Phvs. Rev. 21, 1169 (1905); Phys. Zeits. 6, 610 (1905). 



Chemical and Electrochemical Clean-up of Gases at Low Pressures 179 

and then allowed to stand awhile, on restoring the current, no 
initial evolution is found in most cases." 

L. V. Chrisler 20 has also concluded that the absorption in 
the discharge tube occurs at the anode. On the other hand, the 
weight of evidence points to the predominating influence of the 
cathode on the amount and rate of absorption. B. Hodgson 19 
and S. Brodetsky and Hodgson 15 have investigated the relation 
between amount of clean-up and current, and also the effect of 
varying the chemical composition of the electrodes. The amount 
of gas absorbed per coulomb was observed to increase with 
decrease in pressure, as had previously been observed by Willows. 
The pressures at which these experiments were carried out varied 
from 2 mm. to 0.03 mm. approximately. A battery giving about 
3200 volts was used as source of current, and the actual current 
strength varied from 0.008 to 0.002 amp. They found that the 
absorption varied with the rate of disintegration of the cathode, 
and no absorption was obtained in absence of such disintegration. 
Furthermore, the absorption was observed to increase with 
increase in cathode drop. They therefore concluded, in agree- 
ment with Soddy and Mackenzie, that the major portion of the 
clean-up is due to adsorption of the gas by the metal sputtered 
from the cathode. 

These observations have been confirmed to a large extent 
by L. Vegard. 4 He finds that absorption is small as long as the 
cathode drop is below a certain "threshold" value, and he con- 
nects the clean-up with cathodic sputtering. The absorption 
rate follows the cathode drop and runs parallel with the amount 
of cathodic sputtering. Thus, in oxygen gold electrodes show 
more sputtering than electrodes of platinum. At the same time, 
the rate of clean-up is greater with gold than with platinum. 
Vegard also observed that in the case of helium there is a measur- 
able clean-up which is, however, less than that obtained under 
similar conditions with either nitrogen or oxygen. In the case 
of hydrogen both absorption and evolution were found to occur. 
1 ' When a current of definite value has reduced the pressure to a 
given value, a larger current causes evolution, and a smaller one, 
absorption." This probably accounts to a certain extent for 
Skinner's observations. 33 Vegard concludes from his experi- 
ments that absorption occurs at the cathode and is somehow 
caused by high velocity positive ions impinging on the cathode. 
In other words, his explanation attempts to compromise between 
both the chemical and the mechanical theories. 



" Ann. d. Physik, 50, 769 (191 1 



180 Chemical and Electrochemical Clean-up of Gases at Low Pressures 

ELECTRICAL CLEAN-UP OF GASES AT LOW PRESSURES 

As mentioned previously, an ordinary discharge tube with 
cold electrodes becomes inoperative when the pressure is reduced 
to too low a value. In general, this occurs at pressures which 
range from 1X10 -3 to 100 X10 -3 mm. of mercury, depending 
upon the nature of the gas and the maximum voltage of the source 
of current. The operation of such discharge tubes depends 
primarily upon the formation of positive ions by the disruptive 
action of the voltage; and the bombardment of the cathode by 
these positive ions causes the emission of electrons which in turn 
ionize more gas molecules, so that the discharge is apt to become 
quite unstable. In the preceding section we discussed clean-up 
effects in such discharges at relatively high pressures. Within 
the past few years, however, a type of vacuum tube has been 
developed in which conduction occurs by means of electrons 
emitted from an incandescent cathode. The pressure in these 
devices must be maintained at a low value, ordinarily below 
10~ 2 bar (10 -5 mm. approximately). Consequently it is of 
practical importance to consider the changes in gas pressure 
which are observed in the operation of such tubes. The study of 
these phenomena is also of theoretical importance because it 
throws light, as will be shown, on certain clean-up effects in 
vacuum type incandescent lamps. 

Electron Emission Phenomena at Low Pressures 35 

The electron emission from a heated cathode increases with 
the temperature according to the equation, first derived by 
Richardson : 

i = A\/fe~ b/T (53) 

where i — electron emission per unit area, and A and b are con- 
stants for any given material. I. Langmuir has shown that the 
actual magnitude of this emission at any temperature, that is of 
the values of A and b in this equation, is extremely sensitive to 
the presence of slight traces of certain gases and the maximum 
value of the specific emission at any temperature is attained only 

35 The literature on this subject has become so extensive in the past few years that only 
a brief discussion has been considered ample in the present connection. For further ref- 
erences, consult the following books and articles: 

(a) O. W. Richardson, "The Emission of Electricity from Hot Bodies," 1.916. 

(b) H. J. Van der Bijl, "Thermionic Vacuum Tube," McGraw-Hill Book Co.. 1920. 

(c) I. Langmuir, General Electric Review, 18, 327 (May, 1915), 23, 503, 589 
(June and July, 1920). 

(d) I. Langmuir, Phys. Rev. 2, 402, 450 (1913). 

(e) S. Dushman, General Electric Review, 18, 156 (March, 1915). 

(f) S. Dushman, Phys. Rev. 4, 121 (1915). 



Chemical and Electrochemical Clean-up of Gases at Low Pressures 181 

in extremely good vacua. In the case of tungsten, the constants 
have the values : 

,4=23X10 9 
6 = 52,500 
where j = milliamp. per cm 2 , and T is the absolute temperature. 
This gives the maximum electron current that it is possible to 
obtain from a unit area of tungsten at any definite temperature. 
It was observed by Langmuir that in addition to this limita- 
tion due to temperature, there is also present, at very low pres- 
sures, a voltage limitation, due to a "space charge" produced 
by the electrons in the neighborhood of the cathode. The elec- 
tron current is then limited by the anode voltage V, in accord- 
ance with a relation of the form : 

i = kV (54) 

where k is a constant whose value depends upon the geometrical 
arrangement and shape of the electrodes. This relation gives the 
minimum voltage between anode and cathode at which a given 
electron current can be obtained in the particular tube, under 
good vacuum conditions. 

Ionization Effects 

When, however, the gas pressure exceeds a certain value 
(depending principally upon the nature of the gas and the 
geometrical dimensions of the device) some of the electrons no 
longer travel directly from the cathode to the anode. Collisions 
with gas molecules occur, and if the anode voltage exceeds the 
so-called ionizing potential 36 positive ions are produced, which 
tend to neutralize a part or the whole of the negative space charge 
produced by the electrons and consequently the electron current 
reaches the saturation value corresponding to the temperature 
of the filament, at much lower voltages than when gas is not 
present. 

These phenomena are illustrated by the following observa- 
tions with a small hot -cathode high-vacuum rectifier (kenotron) 
in which a tungsten spiral was used as cathode, and a molyb- 
denum cylinder (enclosing the spiral) as anode. To the bulb 
containing these electrodes was attached an appendix containing 
a small amount of mercury, and the whole arrangement was 
exhausted to a very high vacuum. By immersing the appendix 

36 For each gas it has been observed that there exists a definite voltage at which the 
electrons acquire sufficient velocity to produce positive ions by collisions with gas mole- 
cules. These voltages have been measured for a number of gases and metallic vapors, and 
they are found to vary from about 25 volts in the case of helium to approximately 4 volts in 
the case of the alkali metals. See the report on "Photo-electricity and Ionization Poten- 
tials," by A. LI. Hughes, Bull. Nat. Res. Council, 2, 83 (1921). 



182 Chemical and Electrochemical Clean-up of Gases at Low Pressures 

in liquid air the pressure of the mercury vapor could be reduced 
to such a low value that no ionization effects occurred. Fig. 68 
shows the characteristics of the tube under these conditions, at 
two different filament currents. It will be observed that at 1.35 



AR 


























/ 
































/ 
































/ 
































,/ 


' 
































/ 












40 






















/ 






































h C 








36 




























/ 


S 






















1 








/ 


























1 






/ 


























/ 


















m 
















1 
































1 




















v 








c 




A 


1 




'b 
















o 












/ 






















< "° 












/ 


/ 
































/ 






























1 


1/ 


f 






















19 








/ 


// 




























Blu 


jGI 






























w y 
































































































































n 



































16 



24 32 40 48 
Anode Volts 



56 64 



72 



Fig. 68. Illustrating Effect of Mercury Vapor on 
Characteristics of Hot Cathode Tube 

Curve .A — Space charge limitation in good vacuum 
Curve B — Space charge and temperature limitation 
Curve C — Same filament temperature as Curve B. 

but in presence of mercury vapor at 

a pressure of two bars 



amp. (Curve A), the electron current varied with the anode 
voltage in accordance with the 3/2 power relation. At 1.25 
amp. the electron current increased at first in accordance with the 
same voltage law and then tended to reach the value 38 milli- 
amp. corresponding to the emission for that particular tem- 
perature (Curve B). 



Chemical and Electrochemical Clean-up of Gases at Low Pressures 183 

On removing the liquid air from the appendix, so that the 
mercury attained room temperature and the pressure in the 
device reached the value of about 2X10 -3 mm. (corresponding 
to the vapor pressure of mercury at this temperature) , the char- 
acteristic obtained with the filament at 1.25 amp. was that shown 
in Curve C. At 18 volts a distinct blue glow appeared, and at 
26 volts this glow extended practically all the way down the 
appendix. It will be observed that simultaneously with this 
appearance of blue glow, the electron current increased rapidly 
until it reached practically the same saturation value as that 
obtained under good vacuum conditions. That is, even at such a 
low pressure of mercury vapor, the space charge phenomena 
practically disappeared and the saturation electron emission 
corresponding to 1.25 amp. filament current was obtained at 
relatively low voltages. 

Observations on Clean-up in Hot-cathode Devices 

Similar phenomena are observed with all other gases in 
hot-cathode devices. At very low pressures the electron current 
varies with the voltage according to the 3 (2 power law, but at 
higher pressures (ordinarily about one to two bars) blue glow 
appears as the voltage is raised above the ionizing potential and 
simultaneously with this blue glow the current increases rapidly, 
as shown in Curve C, Fig. 68, to the saturation emission at the 
given filament temperature. In the case of most gases this blue 
glow does not ordinarily persist very long, owing to clean-up 
effects that accompany the appearance of this glow, and con- 
sequently the electron current decreases again gradually until 
it attains the limiting value corresponding to the space charge. 

These clean-up phenomena that are observed in hot-cathode 
devices are entremely interesting, and they are of great technical 
importance. The experimental evidence which has been obtained 
in this laboratory and by other investigators points to the con- 
clusion that these effects are primarily due to the formation of 
ions by collisions between electrons and gas molecules. There 
is little or no evidence for any electrical clean-up below ionizing 
potentials. 

Experiments along this line carried out in this laboratory for 
the past few years have shown that the factors governing this 
clean-up are quite complex. In general, the rate of clean-up 
shows a tendency to increase with the anode voltage and with 
the electron current. In addition to these factors, the condition 
of the glass walls and the previous history of the bulb exert a 
profound effect on the rate of clean-up. The disappearance 



184 Chemical and Electrochemical Clean-up of Gases at Low Pressures 

of gas by electrical clean-up is observed even at the very low 
pressures where space charge effects are present and blue glow is 
therefore absent. Numerous observations in connection with 
hot -cathode devices, such as are made up in this laboratory, have 
confirmed this conclusion. Thus a kenotron (hot-cathode 
rectifier) may be sealed off at 0.05 bar and by subsequently 
operating it with a current of a few milliamperes at 120 to 240 
volts, the pressure will be found to decrease to 0.01 bar or less. 
-At any given electron current the residual gas pressure in 
the sealed off tube reaches an equilibrium value which increases 
with the electron current. Part of this increase is probably due 
to an increased rate of evolution from metal parts and glass walls 
until equilibrium is attained with the increased rate of clean-up. 
The pressure may thus be found to vary from 0.01 to as low as 
0.0001 bar, depending upon anode voltage and electron current. 
Similar effects have been observed with the ionization gauge 
in using it to measure low pressures of chemically active gases, 
such as nitrogen, hydrogen, and oxygen. That this clean-up is 
not due in these cases to purely chemical reactions at the surface 
of the tungsten filament is easily shown by taking off the anode 
voltage, when the clean-up practically ceases. Moreover this 
clean-up also occurs with the inert gases argon and helium. 

A preliminary account of some recent observations made by 
Mrs. M. Andrews, H. A. Huthsteiner, and the author, on this 
subject, may be of interest in this connection. In these experi- 
ments a tube containing two adjacent tungsten filaments was 
used, so that either filament could be made cathode, and the 
rate of clean-up was investigated in the case of argon and 
nitrogen. Gas from a large reservoir was allowed to flow con- 
tinuously through this tube at practically constant pressure, 
and the rate of clean-up was determined by collecting the gas 
after it left the tube. The pressures used in most of the experi- 
ments were so low that no blue glow effects were observed, and 
during any one set of observations both the electron current and 
the anode voltage were maintained constant. The magnitude 
of the current was varied in different runs from a few micro- 
amperes to several milliamperes, and the anode potential was 
varied from 25 to 250 volts. The rate of clean-up was observed 
in these experiments to increase almost linearty with increase in 
pressure. With electron currents below a milliampere, the rate 
of clean-up also varied linearly with the current, but showed a 
tendency to increase much less rapidly with electron currents 
exceeding this value. At anode voltages in excess of 25, the rate 
of clean-up was observed to be practically constant and inde- 



Chemical and Electrochemical Clean-up of Gases at Low Pressure: 



185 



pendent of the voltage. With freshly baked out glass bulbs, the 
fatigue effects observed were quite pronounced. On covering 
the glass surface inside with a tungsten deposit (by evaporation 
of one of the filaments) the rate of clean-up was found to increase 
considerably, and much more gas could be cleaned up before 
fatigue effects occurred. The rate of clean-up of argon was 
found to be about half of that of nitrogen under otherwise similar 
conditions. 

The following observations were made on a system con- 
sisting of a five-inch bulb containing two adjacent tungsten 
filaments to which was attached an ionization gauge. The 
volume of the arrangement was about 1200 cm 3 . After a thorough 
exhaust on the condensation pump, followed by a flashing of the 
filaments at a high temperature, argon at a pressure of 1.35 X 10 -3 
mm. of mercury was let into the system and the whole sealed off 
the pump. One of the tungsten filaments was then made cathode 
and raised to the temperature necessary to give an electron 
emission of five milliamperes. With 250 volts on the other 
filament as anode, the pressures indicated in the following table 
were obtained at different intervals of time. 



Time 
/ (minutes) 


Pressure 
mm. X10 -3 


k=jlog(p /P) 




2 

4 

15 

27 


1.35 
1.2 

1.05 
0.65 
0.36 


0.0255 
0.0273 
0.0212 
0.0213 






Avg.= 0.0238 



The constancy of k in the last column shows that the rate 
of clean-up at any instant was proportional to the pressure. 

Observations were made in the same manner with nitrogen. 
In one experiment, using 5 milliamp. and 250 volts, the nitrogen 
cleaned up from a pressure of 8X10 -3 mm. to 1X10~ 3 mm. in 
36 minutes. In all these cases, if after cleaning up a certain 
amount of gas, more gas was let into the bulb, the rate of clean-up 
was observed to be much lower. 

Regarding the mechanism of this clean-up, it is difficult 
to draw any positive conclusions. In the foregoing experiments 
there was no evidence to show that the gas was cleaned up at the 
cathode, as for instance by the formation of WN 2 . This would 
certainly not be true in the case of argon; the gas was most 




186 Chemical and Electrochemical Clean-up of Gases at Low Pressures 

probably driven into the walls. Subsequent heating rarely 
caused the evolution of as much gas as had been cleaned up, 
so that the ions must penetrate the glass quite deeply. 

Observations similar to those mentioned have been made by 
other investigators working with hot -cathode devices. Thus 
W. H. Eccles, in a discussion on thermionic valves, 37 makes the 
following very interesting comments regarding clean-up effects: 

' ' Many interesting phenomena are observed with the traces 
of residual gases always present even in the hardest of tubes. 
After running for some time with a given electron current to the 
positive electrode and a given voltage, a steady value for the 
pressure of the residual gas may be reached. If now the voltage 
is increased, but not sufficiently to overheat the positive elec- 
trode, the tube will harden, i.e., some of the residual gas will be 
absorbed. On the other hand, if the voltage is reduced, and 
particularly if the filament is simply heated without any voltage 
being applied to the positive electrode, the amount of residual 
gas will increase. 

"These effects are well known to radiologists and various 
suggestions are put forward in explanation. But from the point 
of view of the development of the high-power valves, the whole 
problem requires careful investigation. 

"The fact that an increasing voltage at the positive elec- 
trode hardens the valve leads to the conclusion that the effects 
are due to the action of the ionized gas. At these voltages the 
ions are positive, and their observed disappearance must be due 
to their being driven into the hot filament, or into the walls of 
the containing vessel. If they are driven into the filament, how 
are they retained with the filament at 2000 deg. C? Is any 
chemical action involved, or is it the same process as the occlusion 
in the positive electrode ? Or is it only the walls of the containing 
vessel that absorb the ions ? 

"A suggestion has been put forward by Dr. G. B. Bryan of 
the Physics Laboratory, at Royal Naval College, Greenwich, 
that the occlusion of the gases and the emission of positive ions 
from metallic surfaces at moderate temperature are closely 
related. He visualizes the process as follows : Some proportion 
of the gas to which the electrodes are exposed will probably be 
ionized hydrogen. A positive hydrogen ion is a very small heavy 
projectile with considerable powers of penetration. On striking 
the surface of a solid it will pass through the outer surface and 
pick up an electron, so becoming neutral. Now, however, it is a 

" The Radio Review, 1, 26 (1919). 



Chemical and Electrochemical Clean-up of Gases at Low Pressures 187 

large body entrapped in among the atoms of the metal and unable 
to escape under ordinary conditions. But at moderate tem- 
peratures the electrons may be shed again, and the positive ion, 
being no longer encumbered by the outlying electron, can escape, 
so constituting the positive emission. One peculiar faot has 
frequently been observed by Dr. Bryan when exhausting a valve, 
viz., that a small liberation of occluded gas will give rise to a 
greater tendency to arcing than the introduction of a much 
greater quantity of ordinary air. If the gas liberated from the 
electrodes is already ionized, the observation is immediately 
explained. 

''This theory is a very interesting one, and is one on which 
some light could be thrown by the entire removal of all traces of 
hydrogen. At present, however, it has never seemed possible 
to do this, as such extremely small quantities are involved; and 
possibly other ionized gases may be entrapped in the same way. 
If it is the outer electron that is lost, this would seem to be quite 
possible." 

That the positive ions attain, under even moderate voltages, 
velocities which are much greater than those possessed by the 
corresponding molecules at ordinary temperatures, has already 
been pointed out in the discussion of electrical clean-up at higher 
pressures. It is therefore interesting to observe that Eccles and 
Bryan also consider that this may be a possible explanation of the 
observed clean-up effects in hot-cathode devices. 

On the other hand, in a very recent paper by A. LI. Hughes 38 
another explanation has been made which is to a certain extent 
equally probable. In these experiments the electrical clean-up 
of nitrogen and hydrogen was studied in a tube containing as 
cathode a platinum filament coated with BaO and SrO. In most 
of the experiments the whole tube was kept immersed in liquid 
air and the electron current was maintained constant in any one 
set of measurements. The rate of clean-up was found to decrease 
gradually during any run, owing to gradual saturation of the 
walls of the tube (as in the experiments mentioned previously. The 
initial pressures used in these experiments varied from 50 X 10 -3 
mm. to 2X10 -3 mm. of mercury. The conclusions as stated by 
Hughes are as follows : 

"For hydrogen, no disappearance was obtained unless the 
electrons had energy above 13 volts. The rate of disappearance 
rose rapidly as the energy of the electron was increased to about 
70 volts, after which no rapid change was noted (the rate ap- 

«« Phil. Mag. 41, 778 (1921). 



188 Chemical and Electrochemical Clean-up of Gases at Low Pressures 

peared to diminish somewhat when the energy of the electrons 
was raised from 150 to 300 volts). For nitrogen, the rate of 
disappearance was at first much less than for hydrogen, but when 
the energy of the electrons was raised sufficiently (roughly 200 
volts) the rate of disappearance of the nitrogen exceeded that for 
hydrogen." 

In explanation of the mechanism of clean-up Hughes con- 
cludes that "this disappearance is due to the splitting of the 
molecules into atoms when electrons collide with the molecules, 
and these atoms condense on the adjacent surfaces particularly 
if they are cold." This explanation would account for the 



0.20 

0.15 

J0 0.10 

0.05 



50 







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v*}i 


ro32 








// 












/ 













100 150 200 

Acccleratinq Volts 



250 



300 



Fig. 69. Hughes' Experiments on Clean-up of Gases. 
Variation with voltage in the ratio (b) of the 
number of molecules cleaned-up to the number of 
collisions between electrons and molecules 



observations made in the experiments of Mrs. Andrews and 
Huthsteiner that a charging up of the tungsten deposit on the 
walls, with either positive or negative potentials, produced no 
effect on the rate of clean-up of nitrogen. On the other hand, 
such an explanation could obviously not account for the clean-up 
of argon. Hughes has also calculated the ratio between the 
number of molecules disappearing and the number of collisions 
between electrons and molecules. Fig. 69 taken from his paper 
gives the relation between the value of this ratio (designated b) 
and the anode voltage for both nitrogen and hydrogen. It is 
seen that with approximately 250 volts on the anode, about one 
molecule disappeared for every six collisions, and presumably 
this molecule disappeared in the form of atoms. The theory that 
collisions between electrons and molecules may not only lead to 
the formation of ions but also to a dissociation of these molecules 
is extremely suggestive and may be a satisfactory explanation 
of the clean-up effects in some cases, but it is hardly possible 
that it is of general application. 



Chemical and Electrochemical Clean-up of Cases at. Low Pressures 189 



Clcan-up and Glow Phenomena 

The disappearance of gas in hot-cathode devices has also 
been discussed at considerable length in three papers by the 
research staff of the General Electric Company, Ltd., London. 39 
In the first one of these papers, after discussing the previous 
work on clean-up phenomena in electrical discharge tubes and 



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200 300 *00 500 600 700 800 900 1000 

l/p(N 

f>« .Q-OIW.KI 0-003 0-002 fiOQL 

Fig. 70. Relation between Pressure and Glow Potential for Various Gases (Campbell) 



• 200 



Langmuir's work on purely chemical clean-up, the writers point 
out the effect of gas in eliminating space charge, as has already 
been described and lay special stress upon the appearance 
of the glow as an essential factor for the occurrence of clean-up. 
Accordingly they have made very careful measurements of the 
potentials at which this glow occurs. "The first observations," 
it is stated, "proved that the glow potential is independent of 
the temperature of the filament and of the thermionic emission 

M N. R. Campbell, Phil. Mag. 41 , 685 (1921); N. P.. Campbell and J. W. H. Ryde, ib. 
40, 585 (1920); ib. 41, 2 27 (1921). Observations on the clean-up effect in presence of blue 
glow are also recorded by C. F. Hagenow, Phys. Rev. IS, 415 M919). 



190 Chemical and Electrochemical Clean-up of Gases at Low Pressures 

from it in wide limits. If there is no thermionic emission, the 
glow does not appear of course until the spark potential of the 
gas is reached, but the change from this condition to that in which 
the glow occurs at the very much lower potential obtained with 
a hot-cathode is so rapid that it could not be determined certainly 
whether the change was continuous or discontinuous. Once the 
lower value is obtained, no further change occurs even if the 
thermionic emission is increased 100-fold. There is no evidence 
that the glow potential depends at all on the thermionic emission, 
so long as it is great enough to give at all a glow potential distinct 
from the spark potential. On the other hand, the glow potential 
depends greatly on the pressure, and on the nature of the gas. M 

Fig. 70 shows the relation obtained in this investigation 
between the pressure and the glow potential for different gases. 
It will be observed that the potentials are plotted against the 
reciprocal of the pressures. The argon used contained 
five per cent nitrogen. The curves for hydrogen show the effects of 
slight traces of impurities. The glow potentials observed with in- 
creasing voltages were invariably somewhat higher than those 
observed with decreasing voltages, the maximum difference 
being obtained in the case of argon where it was about 10 volts 
at a pressure of 5X 10~ 3 mm. of mercury. 

In the case of mercury vapor the glow potential was observed 
to be always 32.5 volts, "whatever the nature of the gas with 
which it is mixed." Furthermore the addition of any impurity 
to a gas was often observed to decrease the glow potential below 
that of either of the constituents. 

An important distinction is drawn by these investigators 
between the glow potential and that required for ionization. 
"It is clear that the glow potential is not, like the ionization 
potential, a direct property of the individual atoms of the gas, 
it must also be a function of their mode of reaction with each 
other or with the walls of the vessel; for the glow potential is not, 
like the ionization potential, independent of the pressure. There 
is no evidence, therefore, that the glow represents a new form of 
ionization of the individual atoms." 

Some interesting observations are recorded on the rate of 
disappearance of different gases in the presence of a glow dis- 
charge. In the case of CO, it was found that the gas cleaned up 
in consequence of the reaction, 2CO = C + C0 2 , the carbon 
dioxide formed being adsorbed on the glass walls. The com- 
plete elimination of mercury vapor is essential for the occurrence 
of this reaction. "If mercury vapor is completely removed, the 
disappearance continues until the discharge stops, owing to the 



Chemical and Electrochemical Clean-up of Gases at Low Pressures 191 

rise of the glow potential — at any rate, if a potential greater than 
300 volts is not employed. If fresh CO is admitted, it disappears 
again under the discharge at a rate apparently unchanged; a 
limit to the absorption has not been found, although a quantity 
has been adsorbed equal to at least five times that representing 
a monomolecular layer on the walls." On baking the vessel to 
over 330 deg. C, the greater part of the gas was re-evolved, 
mostly as C0 2 . 

Nitrogen was observed to disappear in the same manner as 
does carbon monoxide, "in apparently unlimited quantities." 
This is accompanied by some decrease in the filament diameter 
and a blackening of the bulb. Probably WN 2 is formed as has 
been shown by Langmuir, 40 although Campbell seems inclined 
to believe that the tungsten is cathodically sputtered off the 
filament and covers the nitrogen which is adsorbed on the glass. 

The rate of clean-up of argon was observed to be less than 
one-fifth that of nitrogen, and at the same time rapid blackening 
of the bulb occurred. "In both nitrogen and argon there is the 
intimate connection between cathode sputtering and absorption 
of gas which Vegard 41 has noted in the discharge without an in- 
candescent cathode." 

The observations with hydrogen in the absence of a dis- 
charge were in agreement with Langmuir 's observations on the 
formation of atomic hydrogen. 42 Campbell finds, however, that 
in the presence of a discharge the rate of clean-up is much less 
than that obtained because of purely thermal dissociation. 

Very interesting phenomena were observed on passing a 
discharge in mercury vapor. In an otherwise thoroughly ex- 
hausted glass bulb, it was observed that under these conditions 
hydrogen is liberated from the walls. The fact that the discharge 
may evolve gas from the walls instead of causing it to disappear 
had already been noticed by Campbell as occurring to some 
extent in nitrogen, CO, and argon. In the presence of mercury 
vapor this phenomenon is extremely marked. 

"And it should be noted that the gas thus liberated cannot 
be liberated by mere heating of the walls to their softening point ; 
gas can be attached to the walls in soms such way that it can be 
liberated by the discharge but not by heating. Of course, the 
attachment may consist of chemical combination; it is possible 
that glass contains hydrogen chemically combined, probably as 
water. But it should be observed that the hydrogen liberated, if 

«• J. Am. Chem. Soc. So, 931 (1921). 

« Ann. d. Phys. 50, 769 (1916). See also p. 179. 

« J. Am. Chem. Soc. 37, 1161 (1915). 



192 Chemical and Electrochemical Clean-up of Gases at Low Pressures 

piled up on the glass, would form a layer at least 25 molecules 
thick ; some of it must therefore have come from a layer at least 
25 molecules deep. Since the potential driving the discharge in 
these experiments was often as low as 50 volts, it is hardly to be 
expected that the electrons or ions could penetrate so far into the 
glass simply in virtue of the energy which they receive from the 
discharge. It seems easier to believe that a layer on the surface, 
subject to the action of these particles, is constantly renewed by 
diffusion from within." 

The conclusions drawn by Campbell from these experi- 
ments are as follows : 

' ' (a) All gases can be made to adhere to glass by the dis- 
charge in such a way that part, at least, can be restored by heat- 
ing the glass. 

" (b) The amount of gas that can be made so to adhere 
depends on the nature of the gas and on the state of the glass. 

"(c) The adhesion is not due primarily to chemical re- 
action, although such reaction (as in the conversion of CO to 
C0 2 ) may aid adhesion by converting the gas into another which 
adheres more readily. 

"(d) The discharge can also liberate gas from the walls, 
doubtless by bombardment of the charged particles, and some of 
the gas so liberated cannot be liberated by heating the glass to 
the softening point. 

' ' (e) The limit in the disappearance of the gas is reached 
when the rate at which gas is caused to adhere to the glass by the 
discharge becomes equal to the rate at which it is liberated by 
the bombardment." 

The second paper referred to above deals with the theory 
of clean-up in presence of phosphorus vapor, and is discussed in 
a subsequent section. In the third paper, Campbell again takes 
up the problem of glow potentials and the relation between 
primary electron and ionization currents. The most important 
result obtained in this investigation is the demonstration that,, 
"in a discharge vessel with electrodes, of which the area is small 
compared with that of the walls, those walls can act as a third 
electrode, receiving almost all the positive ions, the charge on 
which is neutralized by electrons from the cathode." By coating 
the inside wall of the two-electrode tube with a deposit of silver 
and charging the latter with a small negative potential (with 
respect to the hot cathode) it was possible to measure the positive 
ionization current produced by any definite electron current 
between the hot cathode and anode. Fig. 71 illustrates a typical 
series of observations at a pressure of 0.156 mm. of CO. The 



Chemical and Electrochemical Clean-up of Gases at Low Pressures 193 



a 
E 
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-p 
|.02 

O 



.01 



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10 20 30 

v (volts) 



40 



Fig. 71. Typical Series of Observations at a Pressure of 0.156 mm. of CO. 



194 Chemical and Electrochemical Clean-up of Gases at Low Pressures 

electron current, i e , rises steadily from the ionization to the glow 
potential, but the positive ion current, i,., is barely perceptible 
until just before the glow potential. At the glow potential, both 
i e and i e rise rapidly. If the third electrode is insulated, it is 
observed to charge up to approximately the same potential as 
the cathode, and nearly all the positive ions travel to it, as shown 
by the magnitude of i g , when this electrode U connected to the 
cathode through a galvanometer. That this third electrode must 
also be receiving electrons in quantity to neutralize the charge 
of the positive ions is evidenced by ttn observation that "at 
higher pressures, though the current and energy carried by the 
discharge may be sufficient to melt the anode, the latter does not 
become visibly hot; all the heat is communicated to the walls." 
In this respect all observations made in this laboratory on the 
electric discharge in hot cathode devices in presence of gas are 
in accord with Campbell's conclusion. It is interesting to note 
that Campbell finds the ratio i s ji e to be practically independent 
of pressure until the pressure falls so low that the applied voltage 
is below the glow potential. On the other hand, as shown by the 
measurements of C. G. Found and S. Dushman with the ioniza- 
tion gauge the ratio varies directly with the pressure for pressures 
below that at which blue glow occurs.* 

The relation between the positive ionization and the rate of 
clean-up of CO gas (previously referred to) was studied from this 
point of view and the conclusion drawn that the production of 
C0 2 from CO by the discharge takes place by the collision of a 
positive CO ion with a neutral CO molecule. Thus, for every 
positive ion arriving at the grid, there is a disappearance of two 
molecules of CO, namely, the ion itself and a neutral molecule. 

The results of some experiments carried out in this labora- 
tory are of interest in connection with these observations ob- 
tained by Campbell and his associates. That the clean-up effects 
are more pronounced in the presence of blue glow is undoubtedly 
true but, as already mentioned, the rate of electrical clean-up 
in hot-cathode devices is quite appreciable even at low pressures 
where the voltages used are below the corresponding glow 
potential. Again, the actual values of the glow potentials as 
given in Fig. 70 are probably dependent upon the form of the 
electrodes and the vessel, a conclusion which is also expressed by 
Campbell. Thus, the glow potential for mercury at 2X10 -3 
mm is given by the latter as 32.5 volts, whereas, as before stated, 
concerning experiments carried out in this laboratory with a 

* See Chapter III, pp. 119-120. 



Chemical and Electrochemical Clean-up of Gases at Low Pressures 19-5 

different construction of hot-cathode tube from that used by 
Campbell, blue glow has been observed at as low as IS volts. 

With regard to the relation between blue glow potential 
and electron emission, Mrs. Andrews* has observed that in the 
case of both argon and nitrogen the voltage required for the 
appearance of blue glow shows a tendency to decrease with 
increase in emission. At higher pressures it is possible to observe 
two glow potentials; at the lower of these, blue glow appears 
below the anode, and at the upper voltage the glow occurs both 
above and below the anode. Furthermore, with 250 volts on 
the anode, it was observed that the electron emission at which 
blue glow appeared varied approximately inversely with the 
pressure. Thus, at 45 X 10~ 3 mm. of argon, the electron emission 
required to produce blue glow was about 0.15 milliamp., whereas 
at 4X10 -3 mm. the necessary emission was about 1.4 milliamp. 
In these measurements an ionization gauge was used, with the 
inner filament as cathode and the other one as anode. At the 
same time the positive ion current was measured to the cylinder 
surrounding both filaments, and it was observed that this current 
was approximately the same in all cases when blue glow appeared. 
This means that for the appearance of glow in any device it is 
apparently necessary to have a certain density of positive ions. 
This conclusion would also be in accord with the observation 
mentioned previously that the electron current required for blue 
glow to appear varies inversely as the pressure. 
Electrical Clean-up Phenomena in Incandescent Lamps 

The observations discussed in the previous section have a 
fundamental significance from the point of view of the clean-up 
effects observed in vacuum type incandescent lamps. 

In European practice it is customary to exhaust lamps to a 
very high degree of vacuum, the residual gas pressure being 
usually less than one bar. Care is taken to eliminate water 
vapor as much as possible by a thorough baking out of the glass, 
and the filaments are flashed on the pumps. On the other hand, 
in this country various economic considerations have led to 
greater and greater speed of production in all lines, not excluding 
that of lamp manufacture. Consequently the period of 
exhaust has been reduced, and at present it is the normal practice 
to complete the whole exhaust operation in a period which may 
vary from five minutes to as low as one-half minute. In this 
short period of time the pressure is reduced from atmospheric to a 
few bars, the glass is raised to a high temperature to eliminate 
as much water vapor as possible and the lamp sealed off. 

* A complete account of these experiments will be published in the near future. 



i 



196 Chemical and Electrochemical Clean-up of Gases at Low Pressures 

It is evident that under these conditions there must remain 
in the lamp a considerable amount of residual gas, to which 
must be added the gas that is subsequently evolved on lighting 
the filaments. As a matter of fact, the residual gas pressure in 
actual practice varies from as low as one bar to over 100 bars, 
depending upon the nature of the exhaust process used. In view 
of the fact, which has been known for a longtime, that the life of 
an incandescent lamp is considerably increased by improvement 
in vacuum and through elimination of water vapor, it has there- 
fore been necessary to devise methods by which the residual gas 
can be cleaned up. 

The most usual method of attaining this result is that 
suggested by Malignani in 1894. As used in the days of the 
carbon filament lamp, 43 "this process, in its most perfect form, 
consisted in distilling into the bulb a small amount of some such 
substance as arsenic, sulphur, iodine, or phosphorus. At the 
instant when one of these vapors was introduced, a high current 
was passed through the filament, the lamp being closed from the 
pump. In case of incandescent lamps where the voltage is above 
50 for a fair brilliancy of filament, a blue discharge passes through 
the bulb and this blue quickly disappears when such vapors are 
introduced." 

Further investigation, notably in this laboratory, showed 
that during the disappearance of blue glow there occurred a con- 
siderable improvement in vacuum. It was furthermore observed 
that this blue glow and clean-up also occurs if no phosphorus 
is used. "In improving the vacuum this latter way, however," 
states Dr. Whitney, "it is known that the filament is injured and 
apparently a part of its material has been vaporized. The process 
soon causes blackening of the lamp by carbon." The connection 
between blue glow and Edison currents in carbon lamps is 
also mentioned in the same paper. It was observed that if a 
platinum plate is sealed into a lamp and charged positively, a 
continuous current can flow to it from the negative half, or end 
of the filament, but not from the positive end. The current was 
found to vary with gas pressure and also the relative location 
of the plate in the lamp. At that time, of course, the phenomena 
of electron emission from heated filaments had not been studied 
thoroughly and for this reason no satisfactory explanation of the 
Edison effect could be given. 

■ The observations on electron emission and clean-up effects 
in hot-cathode tubes obviously throw considerable light on this 
phenomenon. The negative end of the filament emits electrons, 

« W. R. Whitney, Trans. Am. Inst. Electrical Eng. 31, 921 (1912). 



Chemical and Electrochemical Clean-up of Gases at Low Pressures 197 

and under the influence of the positive voltage produced by the 
other end of the filament the residual gas is ionized. Hence the 
appearance of blue glow. The positive ions are, then, cleaned up 
rapidly by the action of the voltage, in the same manner as has 
already been described, and the blue glow disappears. 





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12 16 20 
Minutes 



24 



28 32 



Fig. 72. Clean-up of Residual Air in 100-watt, 120-volt 
"Ungettered" Lamp 

A — Initial pressure, 1.33 bar (1 micron) 
B — Initial pressure, 6-67 bar (5 microns) 



The phenomena in tungsten lamps are similar to those 
observed in carbon lamps. While in the older process the phos- 
phorus was distilled into the lamp from a top tube with simul- 
taneous flashing of the filament, the present process consists in 
coating the wire with an alcoholic suspension of red phosphorus 
and some salt (to prevent subsequent blackening by evaporated 



19S Chemical and Electrochemical Clean-up of Gases at Low Pt 



tungsten). After the lamp is exhausted and sealed off, it is 
flashed with gradually increasing voltage, and as the phosphorus 
is volatilized from the filament, blue glow occurs and the residual 
gases are cleaned up. 44 

Before discussing the theories that have been suggested in 

explanation of the function of phosphorus in cleaning up residual 

1.0 



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5 


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Fig. 73. 



12 16 20 
Minutes 
Clean-up of Residual Air in 100-watt, 120-volt 
"GeUered" Lamp 
A — Initial pressure 10 microns 
B — Initial pressure, 5 microns 



gases, it is of interest to mention some of the experimental results 
that have been obtained by H. Huthsteiner and S. Dushman on 
the rate of clean-up of gases in lamps under various conditions. 
Fig. 72 shows the clean-up of residual air in a regular type 100- 
watt, 120-volt lamp in which no phosphorus or other clean-up 



** For similar observations see also S. Dushman, Phys. Re-v 
C. F. Hagenow. ib. 13, 415 (1919). 



123 (1914), 5. 212 (1915). 



.. and Electrochemical Clean-up of Cases at Low Pressures 199 

reagent was used. An ionization gauge attached to the lamp was 
used to measure the pressure. In lamp practice, any substance 
put on the wire or in the lamp for the purpose of either improving 
the vacuum or preventing blackening is known as a "getter." 
In these experiments therefore, of which the results are given 



10:0 



10 



01 



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1 














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15 20 25 
Minutes 



30 35 



40 



Fig. 74. Clean-up of Argon (Curve A) and Air (Curve B) 
in 100-watt 120-volt Phosphorus "Gettered" Lamp, 
Flashed at 144 volts 



in Fig. 72 the lamps were ungettered. Before introducing the 
air at a definite initial pressure, the lamp and ionization gauge 
were well exhausted by baking out at 360 deg. C. for one hour on 
the pump and flashing the filaments to a high temperature, thus 
eliminating gases occluded in the glass walls and filament; the 
electrodes in the gauge were also well bombarded. Curve A 
shows the rate of clean-up with an initial pressure of 1.33 bar 



200 Chemical and Electrochemical Clean-up of Gases at Low Pressures 



"micron,"*) and Curve B with an initial pressure of 6.67 bar 



(i 

(5 microns). The initial flash of blue glow disappeared in a 
fraction of a minute, and as will be observed from the curves 
most of the gas cleaned up in this period. The subsequent rate 
of clean-up was not as rapid. The flashing voltage used was 156 
.joo 



10 



1.0 



0.1 

































' ■—». — A 










i 










k 










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10 



20 



30 
Minutes 



40 



50 



Fig. 75. Rate of Clean-up in Two-filament Kenotron 
Curve A — No red phosphorus, no voltage on second 

filament 
Curve B — No red phosphorus, 250 volts on second 

filament 
Curve C — Red phosphorus on leads of cathode filament 

250 volts on anode filament 



volts, corresponding to 130 per cent of the normal operating 
voltage. 

Fig. 73 shows the results obtained with a similar lamp in 
which red phosphorus was used as getter. In this case the lamp 
and gauge were exhausted as before, then air was let in, the lamp 

* The micron, 1 X10~ 3 mm. of mercury, is used as a convenient unit of pressure in lamp 
practice. 



Chemical and Electrochemical Clean-up of Gases at Low Pressures 201 

removed from the pump, and a suspension of red phosphorus 
in alcohol painted on the leads just below the filament. The 
combination was then re-exhausted, given a five-minute bake 
out at 360 deg. C. and sealed off. On flashing at 156 volts, the 
leads heated up sufficiently to volatilize the phosphorus and the 
clean-up curves shown in Fig. 73 were obtained. 

In these cases, also, most of the gas cleaned up during the 
period of blue glow, and as will be seen by comparing these results 
with those shown in Fig. 72, the initial rate of clean-up is much 
greater in the presence of phosphorus. In the case of the lamp 
sealed off with air at 10 microns pressure, about 97 per cent of 
the gas disappeared in the first minute. 

Fig. 74 shows the difference in the rate of clean-up of argon 
and air. In the case of argon (Curve A) the initial pressure was 
6.5 microns, and in that of air (Curve B) the residual gas pressure 
was 4.5 microns. These observations also show the effect of 
phosphorus in accelerating the clean-up. 

In general, over 90 per cent of the residual gas is cleaned 
up in a lamp during the blue glow period, and the rate of clean-up 
during this time is much more rapid than that obtained sub- 
sequently. The final pressure attained on flashing varies from 
0.01 to 0.001 X10 -3 mm. of mercury. During life the pressure 
continues to decrease very slowly, and even after the filament 
burns out, there is no increase in pressure. 

Observations with different types of lamps have shown that 
there is no appreciable clean-up below 30 volts, but the rate of 
clean-up increases rapidly as the voltage is increased above this 
value, and is extremely rapid in case of 220-volt lamps. 

Theory Regarding Action of Phosphorus in Improving Vacuum 

Any theory regarding the action of the phosphorus in in- 
candescent lamps must primarily take into account the phe- 
nomena observed in hot-cathode devices. Fig. 75 shows some 
results obtained with a two-filament kenotron (similar to that 
used in studying electrical clean-up effects without phosphorus) 
on the clean-up of residual air. Curve A serves as the blank to 
take into account any purely chemical clean-up, while Curves 
B and C show the effect of the presence of phosphorus. These 
observations show definitely that the phosphorus is most effective 
during the blue glow period, as has already been emphasized in 
describing the clean-up phenomena in lamps. The similarity 
between Curves B and C and those obtained in incandescent 
lamps also leads to the conclusion that the clean-up phenomena 
in the latter and in hot-cathode devices must be quite similar 



202 Chemical and Electrochemical Clean-up of Gases at Low Pressures 

in origin, that is, the reactions probably involve the formation 
of ions as an essential intermediate stage. 

The action of phosphorus in a lamp is undoubtedly not very 
simple. It may be partly chemical, as probably some P2O5 is 
formed in the presence of residual oxygen and this would assist 
materially in eliminating water vapor and hydrogen. In some 
experiments carried out by Messrs. Mackay and Huthsteiner, 
it was observed that very large amounts of hydrogen could be 
cleaned up by the action of P2O5 vapor in a lamp and that a 
black deposit was formed on the walls. This deposit was assumed 
to consist of solid compounds of hydrogen and phosphorus, 
although no conclusive evidence for this was obtained. 

Also, as was mentioned in the discussion of clean-up effects 
at higher pressures, it is probable that under the influence of 
the discharge active modifications of the gases are produced 
which react readily with phosphorus. The fact that according 
to Newman, phosphorus, sulphur, and iodine are most effective 
in cleaning up hydrogen, while these three substances have also 
been found to be very efficient "getters" in cleaning up residual 
gas in lamps, lends much support to this point of view. 

Phosphorus itself is a very interesting substance chemically. 
As is well known, it exists ;n at least two forms at ordinary tem- 
peratures — the white and the red. On heating the white to just 
below 247 deg. C, it is converted into the red modification. The 
latter has an extremely low vapor pressure even at 300 deg. C, 
while the white form is quite volatile. Again, on passing a dis- 
charge through the vapor of white phosphorus it is converted 
into the red modification which deposits as a fine yellow to red 
coloration on the walls of the glass bulb. This phenomenon has 
been investigated very fully by V. Kohlschutter and A. Frumkin. 45 

One theory of the action of phosphorus which has some 
foundation is that the phosphorus vapor at the moment of con- 
densation on the glass removes positive ions from the gas in 
much the same manner as C. T. R. Wilson observed in the case 
of supersaturated water vapor. In the latter experiments it 
was found that on suddenly expanding a gas saturated with 
water vapor (in order to condense this vapor) there was a removal 
of ions on the surface of the extremely small drops of water. 

The most recent and most interesting contribution to the 
elucidation of this problem is that published by N. Campbell. 46 
He finds in agreement with other investigators that on passing 

« Zeits. f. Elektrochem. 20, 110 (1914). 

46 Phil. Mag. 14- 693 (1921). A short discussion of this subject has also been published 
by L. Hamburger, Proc. Amst. Acad. Sciences, 21, 1062 (1919). whose observations are on 
the whole similar to those recorded above. 



Chemical and Electrochemical Clean-up of Gases at Low Pressures 203 

a glow discharge through phosphorus vapor, it is converted into 
the red form, which deposits on the walls. Hydrogen, carbon 
monoxide, and nitrogen when mixed with phosphorus vapor 
clean up in the discharge very rapidly and in large amounts. An 
interesting observation (in accord with those made in this labora- 
tory) is that ' 'a lower final pressure can be reached with a given ap- 
plied potential in the presence of phosphorus than in its absence." 
The explanation of this as given by Campbell is as follows : 

"The absorption of gas ceases when the glow discharge 
ceases; and the glow discharge ceases when the falling glow 
potential becomes equal to the applied potential. The admixture 
of phosphorus vapor with the gas increases the pressure corre- 
sponding to any given partial pressure of the gas, and thus de- 
creases the glow potential corresponding to that partial pressure. 
It therefore enables the discharge and the absorption of gas to 
continue when the partial pressure has fallen so low that, if the 
gas were present alone and its partial pressure were the total 
pressure, the potential applied could no longer be sufficient to 
maintain the discharge. When the partial pressure of the gas 
has fallen sufficiently, the phosphorus vapor, and not the gas, 
begins to disappear; and the disappearance of this vapor pro- 
ceeds until the pressure of the phosphorus has fallen so low that 
the discharge can proceed no longer. And when the discharge 
ceases because the falling glow potential has become equal to 
the applied potential, it is not started again except by a very 
great increase of potential, owing to the wide difference between 
the falling and rising glow potentials in this vapor." 

Furthermore, Campbell concludes that the reaction leading 
to the conversion of the phosphorus vapor into the red solid is 
reversible in presence of the discharge. The equilibrium is 
pushed towards the vapor phase when the red phosphorus on 
the walls is bombarded by positive ions, so that "as long as 
there is gas present in considerable quantity the conversion of 
white into red is never complete; there is always enough white 
phosphorus re-evaporating to maintain the discharge; and it is 
only when the gas has been greatly reduced in quantity that the 
equilibrium moves once more towards the solid phase, and a 
complete disappearance of all gaseous molecules is obtained." 

This theory would account for the observation, often made 
in lamp practice, that clean-up effects can be made to occur in 
lamps in which red phosphorus is present on the bulb walls, 
instead of being on the leads or filament. The action in this case 
would be due to the bombardment of the red deposit by positive 
ions, with the resulting formation of a slight amount of vapor. 



204 Chemical and Electrochemical Clean-up of Gases at Low Pressures 

Regarding the chemical theory of the action of phosphorus, 
Campbell concludes that there is no evidence for any such theory 
and gives the following experimental observations to confirm this : 

" (a) If the gas that has disappeared is restored, it is found 
to be in the same chemical state as it would have been if it had 
disappeared in the absence of phosphorus. 

" (b) There is no simple relation between the quantity of 
gas that can be made to disappear and the quantity of phosphorus 
necessary for its disappearance. There is nothing approaching 
to a 'law of constant proportions.' 

" (c) The amount of gas that will disappear depends very 
greatly on the surface condition of the walls of the discharge vessel . ' ' 

As a working theory Campbell suggests that the. red phos- 
phorus covers the deposited gas and prevents it from being 
liberated again by bombardment. At the same time this red 
deposit provides a new surface on which gas can be absorbed. 
That the red phosphorus deposit adsorbs gas even in the absence 
of any discharge has been observed by the writer in a number of 
experiments. 

From the point of view of this theory, it therefore is possible 
to account for the action of red phosphorus as used in lamp 
practice as follows : As well known the ordinary red phosphorus 
undoubtedly contains small traces of the white modification, as 
shown by the formation of P2O5 when it is exposed to air. 
Furthermore, when the glow discharge starts, some of the red 
phosphorus deposited on the walls becomes converted, as already 
stated, into the white form which volatilizes. This assists in 
maintaining the glow discharges at much lower residual gas 
pressures than is possible in the absence of phosphorus. The 
positive ions (or dissociation products according to Hughes) 
formed in the discharge are driven into the walls and immediately 
become covered with the red deposit. The gas pressure is there- 
fore reduced very rapidly and finally reaches a value at which 
no glow discharge can occur with the given applied potential. 

As mentioned by Dr. Whitney, arsenic, sulphur and iodine 
act in a similar manner to phosphorus in cleaning up gas in 
incandescent lamps. In fact any substance that can be readily 
sublimed acts in the same manner. It seems therefore that the 
most plausible theory would be that firstly the vapor formed by 
volatilization of these substances assists in maintaining a glow 
discharge at lower residual gas pressures, and secondly that the 
deposit formed by condensation of these vapors covers the gas 
driven into the walls (whether as positive ions or neutral dissocia- 
tion products) and thus prevents it from being re-evolved readily. 



£05 

CHAPTER VI 
THEORY OF ADSORPTION AT LOW PRESSURES 

Theory of Unimolecular Layer 

In the preceding chapters we have discussed the different 
methods for the measurement and production of high vacua. 
This discussion has to some extent involved a certain amount of 
theoretical consideration of the principles involved, but in the 
main the object has been to present the matter from an experi- 
mental point of view. The theory has been, as it were, a by- 
product of the experiments. 

There has, however, been developed in recent years a point 
of view of low pressure phenomena which is of extreme impor- 
tance for a thorough understanding of the significance of obser- 
vations in this field. 

Although Dr. I. Langmuir developed this theory 1-2 as a 
result of his numerous investigations on the kinetics of chemical 
reactions at low pressures and the effect of these pressures on 
the electron emission from heated solids, he was also inspired in 
this viewpoint by the results obtained by Laue, the Braggs, 
and others, on crystal structure. 

As was first pointed out by these investigators, an examina- 
tion of crystalline substances by means of X-rays leads to the 
conclusion that the atoms in such solids possess regular geomet- 
rical arrangements which correspond to the geometrical struc- 
ture of the crystals themselves. Thus in a crystal of rock salt 
(NaCl), the atoms of sodium and chlorine are arranged at the 
alternate corners of a cube, each atom of sodium being surrounded 
by six of chlorine and each atom of chlorine by six sodium atoms. 
This is in agreement with the observation that sodium chloride 
crystallizes according to the cubical system. 

The method used by the Braggs has been modified and 
applied by A. W. Hull to the investigation of the crystalline 
structure of metals, and at present we have definite knowledge 
regarding the arrangement of the atoms in a large number of 
metals, whenever these occur in the crystalline state. 3 

In order to account for this arrangement of atoms in solids 
Langmuir considers that there exist between these atoms both 



*I. Langmuir, "Chemical Reactions at Low Pressures," J. Am. Chem. Soc. 37, 1139 
(1915). 

2 I. Langmuir, ' 'Constitution of Solids and Fundamental Properties of Solids and Liquids. 
Part I. Solids," J. Am. Chem. Soc. 38, 2221 (1916). 

These papers contain the most comprehensive discussion of Langmuir's theory of 
adsorption and its bearing on other phenomena at low pressures. 

3 A. W. Hull, "The Positions of Atoms in Metals," Trans. Am. Inst. Elect. Eng., Oct. 
10, 1919. 



206 Theory of Adsorption at Low Pressures 

primary and secondary valence forces, 2 the latter differing from 
the former only in degree. It is therefore impossible to speak of a 
molecule of NaCl in connection with a crystal of salt. The whole 
crystal constitutes a molecule whose composition is Na x Cl x , 
where % is infinitely large. Only when the salt vaporizes do we 
have molecules corresponding to the formula NaCl in the gas 
phase. 

According to this point of view the layer of atoms con- 
stituting the surface of a solid would present unbalanced and 
unsaturated valences on their outer side. From well known 
thermodynamical considerations it follows that these atoms 
must tend to rearrange themselves so that the total energy in 
the field surrounding them is a minimum. In this manner we 
perceive that surface energy (surface tension of liquids also) is 
of the same nature as the energy of cohesion which holds the 
atoms together in the solid itself, and both cohesion and surface 
tension are to be regarded from this viewpoint as similar in 
nature to chemical forces. In fact, the distinction between so- 
called physical and chemical forces disappears on this basis. It 
would take us too far beyond the scope of the present discussion 
to mention the application which Langmuir has made of this 
suggestion to account for certain surface tension phenomena of 
liquids, but the subject is extremely interesting. 4 

As shown by Langmuir, "the attractive force between 
atoms in a solid becomes practically negligible when the distance 
between the centers of the atoms becomes twice as great as the 
distance at which the atoms are in equilibrium." This smallness 
of the range of atomic forces compels us therefore to conclude 
that "in general the distance through which the surface atoms 
are shifted from their original positions in the solid is small com- 
pared to the average distance between the atoms. We must also 
conclude that the abnormal surface arrangement is usually 
limited to the surface layer only. The surface of a solid (or 
liquid) therefore does not contain, as is usually assumed, a 
transition layer consisting of several layers of atoms or mole- 
cules in which the density varies by continuous gradations from 
that of the solid to that of the surrounding gas or vapor. Instead 
we find that the change from solid to empty space is most abrupt. 
The surface of a crystal must then consist of an arrangement of 
atoms as definite as that existing in the interior of the crystals, 
although slightly different from the latter. The surface must thus 
be looked upon as a sort of checkerboard containing a definite 



'I. Langmuir, ''The Constitution and Fundamental Properties of Solids and Liquids. 
Part II, Liquids," J. Am. Chem. Soc. 39, 1848 (1917), also "The Mechanism of the Surface 
Phenomena of Flotation," Trans. Farad. Soc. 15, 1 (1920). 



CO 



Theory of Adsorption at Low Pressures 207 

number of atoms, of definite kinds arranged in a plane lattice for- 
mation* The space between and immediately above (away 
from the interior) these atoms is surrounded by a field of electro- 
magnetic force more intense than that between the atoms inside 
the crystal." 

The existence of this field of force at the surface (which as 
before shown is due to the fact that the atoms there have only 
part of their valences satisfied) is according to Langmuir of 
fundamental importance in accounting for all the various 
phenomena that occur at the surface of a solid, such as the 
adsorption of gases, rates of chemical reactions, and the effect 
of gases on electron emission. 

Adsorption is regarded from this point of view as the 
attachment of outside molecules or atoms to the exposed free 
valences of the atoms comprising the surface layer. As shown 
in Chapter I, equations (7a) and (7b), the rate at which gas 
molecules come in contact with a surface is given. by the equation 

I M 

=p y^RT (7c) 

where co denotes the weight of the gas striking unit area per unit 
time, M is the molecular weight of the gas, R the gas constant, 
T the absolute temperature, and p the pressure. 

Langmuir arrives at the conclusion that in almost all cases 
the molecules striking the surface condense on it. That is, there 
is practically little or no reflection. 5 "This holds true at all 
temperatures. The surface film so formed tends to be a continua- 
tion of the space lattice of the solid. On the other hand, evapora- 
tion of such a film is going on as an independent process, being so 
rapid at high temperatures as to keep the surface practically 
clean. Adsorption is a direct consequence of the time lag between 
condensation and evaporation, and is the result of the kinetic 
equilibrium." 6 

Previous investigators had concluded that at the surface 
of a solid we usually have present an adsorbed film of variable 
thickness; that, in fact, the adsorbed film may be a large number 
of molecules (or atoms) thick, and attempts have even been made 
to calculate the density of this condensed gas on the surface. 
According to this older theory the speed of a reaction between 
a gas and a solid would be limited by the rates of diffusion of the 
reacting gas molecules and reaction products through the film. 

*The italics are due to the writer. 

5 I. Langmuir, "The Evaporation, Condensation, and Reflection of Molecules and the 
Mechanism of Adsorption," Phys. Rev. 8, 149 (1916). 

"J. W. McBain, "Theories of Occlusion, and the Sorption of Iodine by Carbon," Trans. 
Faraday. Soc. 14, 1 (1919). 



208 Theory of Adsorption at Low Pressures 

According to Langmuir, however, the thickness of the adsorbed 
film is almost never in excess of one molecule {or atom), and the 
rate of a chemical reaction at the surface of a metal is therefore 
"limited not by the rate of diffusion through the adsorbed film, 
but rather by the rate at which the surface becomes exposed by 
the evaporation of single molecules from an adsorbed layer one 
molecule deep." Similarly, in the case of electron emission, the 
adsorbed film covering the surface to a larger or smaller extent 
tends to lower the emission, and the actual decrease depends 
upon the equilibrium between the rate of condensation and that 
of evaporation of the gas. At low temperatures, where the rate 
of evaporation is lower, the film covers a larger extent of the 
surface, and the decrease is therefore much greater, while as the 
temperature is raised, the area covered by gas molecules de- 
creases and at very high temperatures the emission therefore 
tends to approach that of the metal in a very good vacuum. 

In the following sections we shall discuss the application of 
this theory to the phenomena of evaporation, adsorption, and 
chemical reactions at low pressures. 

Evaporation of Metals in High Vacua 

As has been shown, the rate at which molecules from a gas 
strike a surface is given by equation (7c). 

In the case of most of the metals the vapor is monatomic. 
When such a metal in the solid state is in equilibrium with 
its own vapor, at a pressure p, this equation must give the 
rate at which the atoms from the vapor strike the surface. On the 
other hand, since there is equilibrium there are just as many 
atoms evaporating per unit area per unit time as condense. Con- 
sequently, the preceding equation must give the rate of evaporation 
of the solid at the temperature T, so that by observing the rate 
of decrease in weight of a given filament at any temperature T, 
it is possible to calculate the vapor pressure at this temperature. 
In this manner, Langmuir has measured the vapor pressure of 
metallic tungsten over the range of temperature from 2000 deg. 
K. to 3540 deg. K. 7 and Langmuir and Mackay 8 have obtained 
similar data for the metals platinum and molybdenum. M. 
Knudsen 9 has shown that equation (7c) also holds accurately 
for the case of a clean surface of liquid mercury evaporating 
into a good vacuum. 

Langmuir and Mackay have also applied the same method 
to the determination of the vapor tension data in the case of the 

n. Langmuir, Phys. Rev. 2, 329 (1913). 

"I. Langmuir and G. M. J. Mackay, Phys. Rev. 4, 377 (1914). 

»M. Knudsen. Ann. Phys, 47, 697 (1915). 






Theory of Adsorption at Low Pressures 209 

metals iron, nickel, copper and silver, but have not published 
their results as yet. The method is so extremely simple that it 
ought to find a large field of application in the solution of certain 
metallurgical problems. 

Adsorption at Low Pressures 

The above theory leads to a precise definition of adsorption, 
as distinguished from absorption, occlusion and similar terms 
which are used quite loosely in the literature. We can speak of 
adsorption only as it relates to the gas which is condensed on the 
surface of any solid as a unimolecular layer. As already stated, 
adsorption is the direct result of a kinetic equilibrium between 
the rate of condensation and that of evaporation. ' ' If the sur- 
face forces are relatively intense, evaporation will take place only 
at a negligible rate, so that the surface of the solid becomes com- 
pletely covered with a layer of molecules. In the case of true 
adsorption this layer will usually be not more than one molecule 
deep, for as soon as the surface becomes covered by a single 
J.ayer the surface forces are chemically saturated. Where, on 
the other hand, the surface forces are weak, the evaporation may 
occur so soon after condensation that only a small fraction of the 
surface becomes covered by a single layer of adsorbed molecules. 
In agreement with the chemical nature of the surface forces, the 
range of these forces has been found to be extremely small, of 
the order of 10 -8 cm. That i§, the effective range of the forces is 
usually much less than the diameter of the molecules. The 
molecules thus usually orient themselves in definite ways in the 
surface layer, since they are held to the surface by forces acting 
between the surface and particular atoms or groups of atoms in 
the adsorbed molecule." 10 

The evidence adduced by Langmuir in favor of this theory 
is of a three-fold nature. First, there are "the observations of 
the electron emission from heated filaments in various gases at 
low pressures and of the velocity of chemical reactions in gases 
at low pressures." Second, direct experimental evidence was 
obtained that "thin oil films on the surfaces of liquids, as well as 
absorbed films of substances dissolved in liquids do not normally 
exceed one molecule in thickness. ' ' Third, Langmuir has actually 
carried out measurements on the amounts of gas adsorbed on 
three typical surfaces: those of glass, mica, and platinum, at 
pressures ranging around 100 bars or less. The results of these 
latter determinations are in accord with the above theory. It 



10 I. Langmuir, "The Adsorption of Gases on Plane Surface of Glass, Mica, and Plat- 
inum," J. Am. Chem. Soc. 40, 1361 (1918). 



210 Theory of Adsorption at Low Pressures 

must of course be realized that extreme precautions were taken 
in this investigation to have the surfaces thoroughly freed of 
previously adsorbed gases before letting them come in contact 
with the gas whose adsorption was to be measured. "At room 
temperature the adsorption by mica and glass was negligible, 
certainly not over one per cent of the surface being covered by a 
single layer of molecules. At — 183 and — 118 deg. C, relatively 
large amounts of gas were adsorbed, except in the case of hydro- 
gen, and at the higher pressures used the surfaces tended to 
become saturated with gas. The maximum quantities adsorbed 
even with saturated surfaces were always somewhat less than the 
amounts to be expected in a unimolecular layer. The amounts of 
the different gases adsorbed by saturated surfaces of mica and 
glass were always in the following order : hydrogen, oxygen, argon, 
nitrogen, carbon monoxide, methane, and carbon dioxide. The 
adsorption of these gases was easily and quickly reversible." 

On the other hand, in the case of platinum no adsorption of 
gases could be observed at even — 183 deg. C. until the platinum 
had been previously "activated" by heating to 300 deg. C. in a 
mixture of hydrogen and oxygen. It was then found capable 
of adsorbing oxygen, carbon monoxide, or hydrogen, and the 
maximum quantities adsorbed corresponded to unimolecular 
layers. But the adsorption was not reversible, reactions ap- 
parently occurring on the surface ' ' due to chemical forces of the 
primary valence type." 

Before discussing the theoretical derivation of the relation 
between amount of gas adsorbed and the pressure observed in 
the above experiments, it may be well to point out the reasons 
given by Langmuir for the difference between these results and 
those observed by previous investigators on the adsorption of 
gases by charcoal and glass. "There appear to be three main 
reasons," he states, "which have led these investigators to con- 
clude that adsorbed films are relatively thick. In most cases 
the experiments have been carried out with porous materials, 
such as charcoal, so that it has not been possible to determine 
with certainty the effective absorbing surface. Other workers 
have employed metal foil or other surfaces, of known area, but 
in order to get sufficiently large surfaces, have packed so much 
foil, etc., into small vessels that enormous numbers of capillary 
spaces were formed. They then employed saturated or nearly 
saturated vapors bringing about actual condensation of liquid in 
the capillary spaces. The third cause of error has consisted in 
the use of substances which actually dissolved the vapor thought 
to be adsorbed. The so-called adsorption of water-vapor by glass 
is an example of this kind." 






Theory of Adsorption at Low Pressures 211 

In discussing, in Chapter IV, the sorption of gases by- 
charcoal and glass and also the gas evolution from glass and 
metals at low pressures, a number of observations have been 
mentioned which are in agreement with this theory. It was 
mentioned in that connection that estimates have been made 
by various investigators of the effective surface per gm. of 
activated varieties of charcoal, and that on this basis, the largest 
amount of any non-condensible gas adsorbed by the charcoal 
would correspond to a layer less than one atom in thickness. 
Where the gas adsorbed is nearly saturated vapor (as is the case 
in a large number of the experimental observations), there is an 
actual condensation of liquid in the capillary spaces, so that 
in general we have, in the case of adsorption by charcoal, both 
condensation to liquid in the pores and true adsorption, or surface 
condensation. 

On the other hand, as pointed out by Langmuir, it is hardly 
possible to conceive of charcoal as possessing an "effective sur- 
face," since it is very probable, in view of the observations made 
by Chaney 11 and others, that the porosity of charcoal and 
similar substances extends down to atomic dimensions. 

The sorption of gases by glass has been another case where, 
according to Langmuir, actual solution of gases in the gel-like 
structure has been confused with true adsorption, and the 
experiments on the adsorption of gases by mica confirm this view. 
Adsorption Relations 

In 1909 Freundlich proposed 12 the semi-empirical relation 
between the quantity of gas adsorbed, q, and the pressure, p, at 
constant temperature, which has the form, 

q = k.p 1 ' !n (51a) 

This equation has been mentioned previously in Chapter IV 
in connection with the adsorption of gases on charcoal. For 
low ' pressures or high temperatures, where the quantities ad- 
sorbed are small, the value of - approaches unity, while at high 

n 

pressures or low temperatures it often becomes as small as 0.1. 
These conclusions are well exemplified by the observations made 
by Claude and Titoff on the adsorption of gases by charcoal at 
various temperatures. Thus, referring to Table XVIII, Chapter 

IV, it will be observed that in the case of hydrogen - is approx- 



"Trans. Am. Electrochem. Soc. 36, 91 (1919). See Chapter IV for discussion of these 
observations. 

12 Kapillarchemie Leipzig, 1909. 



212 Theory of Adsorption at Low Pressures 

imately equal to unity at all temperatures and pressures. On 

the other hand, in the case of nitrogen and carbon dioxide, - 

n 

decreases rapidly with increases in pressure and temperature. 
On the whole, the relation has been found to be in very unsatis- 
factory agreement with experimental observations over large 
ranges of pressures. 

Quite recently A. M. Williams 13 has derived relations 
between the pressure, quantity adsorbed, and temperature by a 
combination of arguments based on thermodynamics and the 
kinetic theory of gases. 

For the change in adsorption with temperature he obtains 
the relation 

and for the adsorption isotherm, the relation 



('¥) 



■Aiq (56a) 



The latter may be expressed in the form 

q/p = K<r A « (56b) 

where Ai,A , and K are constants at any temperature. It will 
be observed that for small values of q, that is, small amounts 
of adsorption, the exponential term is practically unity, so that 
at low pressures and high temperatures, the latter equation 
reduces to the simple form, 

q = k.p. (57) 

These relations are found by Williams to agree well with the 
observations mentioned previously on the adsorption of gases by 
charcoal, especially those of Miss Homfray. The kinetic theory 
considerations used in deriving the above relations led Williams 
also to interesting conclusions which are in agreement with 
Langmuir's theory. He finds on this basis that the surface area 
of the charcoal used by Miss Homfray was about 130 sq. meters 
per gram of adsorbent, which appears reasonable in view of the 
fact that activated charcoal has an estimated surface area of 
about 2500 sq. meters per gram. Furthermore, the theory 
enables Williams to determine the range of molecular attraction 
between adsorbent and gas, and he finds this to vary from 3.2 
to 4.1X10 -8 cm., that is, of the same order as the molecular 

1J Proc. Roy. Soc. (Edin.) 39, 48 (1919). 
Proc. Roy. Soc. (London) .%', 287 (1919). 



Theory of Adsorption at Low Pressures 213 

diameter. As already stated, Langmuir arrives at the conclusion 
that these forces must diminish to practically zero at distances 
which are twice as great as the distance at which the atoms are 
in equilibrium. The agreement in conclusions arrived at from 
totally different points of view is certainly striking. 

As discussed above, Langmuir's theory regards adsorption 
as the result of a kinetic equilibrium between the rate of con- 
densation and that of evaporation. On this basis the quantita- 
tive form of the adsorption isotherm, that is, the relation between 
amount adsorbed and pressure, at constant temperatures, 
depends upon the nature of the mechanism of both the condensa- 
tion and evaporation. 14 Langmuir points out that "the surface 
of crystals resembles to some extent a checkerboard, and when 
molecules of gas are adsorbed by such a surface these molecules 
take up definite positions with respect to the surface lattice and 
thus tend to form a new lattice above the old. A unit area of any 
crystal surface, therefore, has a definite number of 'elementary 
spaces,' each capable of holding one absorbed molecule or atom. 
There will frequently be cases where there are two or three 
different kinds of spaces. * * * Each kind of elementary space 
will, in general, have a different tendency to adsorb gases. As 
the pressure of gas is increased the adsorption will then tend to 
take place in steps, the different kinds of spaces being successively 
filled by the adsorbed molecules." The phenomena that may be 
met in the study of adsorption are thus quite varied and may 
often be very complex. It is therefore not to be expected that 
one single equation should cover all cases of adsorption. As an 
illustration of Langmuir's mode of reasoning we shall discuss his 
derivation of the adsorption isotherm for the simplest case of 
adsorption, that in which we have only one kind of elementary 
space and in which each space can hold only one adsorbed 
molecule. 

The number of gram-molecules striking unit area per second 
is, in accordance with equation (7c) 

^M^v^nm (7d) 

A certain fraction of these molecules, which we may call a, will 
condense. Consequently, the rate of condensation on a bare 
surface is a/j,. If represents the fraction at any instant of the 
surface which is bare, the rate of condensation of gas on the sur- 
face is ad. Similarly the rate of evaporation of molecules from 
the surface at this instant is vd u where 0i = l— is the fraction 

"I. Langmuir, J. Am. Chem. Soc. 40, 1361 (1918). 



214 Theory of Adsorption at Low Pressures 

of the surface covered with molecules, and v is the rate o ' evap- 
oration from a surface completely covered. 
At equilibrium, 

adfx=a(l-d l )fJL=pd l (58) 

Let us place 

a 

— —a 
v 

Then 



- l+.M (59) 

But we can write 0i in another form. Let N denote the 

number of elementary spaces per unit area. Then, if q denotes 

the number of gram-molecules of gas adsorbed per unit area of 

surface, 

where iV = 6.062 X10 23 , the number of molecules per gram- 
molecule. 

Substitut'ng for di by means of equations (7d) and (59) it 
follows that 

where 



V2irMRT 

and a = — 

A 

It will be observed that for small values of b, that is, large values 
of v, the above equation tends to approach the form 

q = abp (61) 

That is, when the rate of evaporation is very high (at higher 
temperatures) and at low pressures, we have a linear relation 
between q and p. 

In order to test equation (60a) Langmuir writes it in the 
form 

p 
so that by plotting — against p, the slope of the straight line 

gives -r, that is, v— . In nearly all cases, the value of a 



Theory of Adsorption at Loiv Pressures 215 

is practically unity. Hence it is possible to calculate from the 
observed values of b at any temperature the rate of evaporation 
per unit area. In the experiments with mica and glass, Langmuir 
finds that this relation is in good accord with the observed data 
for all the gases tested. His conclusions with regard to the thick- 
ness of the adsorbed film have already been discussed. 

Instead of calculating the rate of evaporation, Langmuir 

ot 

has calculated the values of cr = — for the different cases. The 

v 

physical significance of this quantity is that it expresses the 
"relative life " of the molecules on the surface. Thus for oxygen 
adsorbed on mica at 90 deg. K., c = 97,000 seconds, while at 
1 do deg. K. , a = 69,000 seconds. In a similar manner it is possible 
to calculate from the vapor tension data the relative life of a 
molecule at the surface of liquid oxygen at any temperature. A 
comparison of the values of a thus calculated for the gases in the 
adsorbed state and the same gases in the liquid state shows that 
the relative life in the first case is anywhere from 10,000 to over 
1,000,000 times as great as in the latter case. "The forces 
involved in the adsorption of these gases are thus very much 
more intense than those holding the molecules of the liquids 
together." 

In a similar manner Langmuir derives relations for other 
cases of adsorption. An interesting case is that in which the gas 
is adsorbed as atoms (e.g., hydrogen by palladium); it is shown 
that under these conditions the amount adsorbed must vary as 
the square root of the pressure even at relatively low pressures. 

It is evident from the previous discussion that in the case of 
porous substances, such as charcoal, no simple adsorption rela- 
tion can hold valid, since we cannot speak of any definite surface, 
and furthermore, depending upon the magnitude of each indi- 
vidual space in such a structure, the rate of evaporation of ad- 
sorbed gas will vary tremendously. 

Evidence for Adsorption Theory from Study of Chemical Reactions at 

Low Pressures 

Most interesting evidence for the unimolecular layer theory 
of adsorption has been obtained by Langmuir in his numerous 
investigations on chemical reactions at low pressures. Some of 
these investigations have been mentioned in Chapter V in 
discussing chemical methods of clean-up. The interest in the 
present connection lies rather in the conclusions which Langmuir 
has derived regarding the mechanisms of these reactions. 



216 Theory of Adsorption at Low Pressures 

Let us consider the reaction between oxygen at low pressures 
and a heated tungsten filament. At any temperature of the fila- 
ment it is observed that the rate of clean-up is proportional to 
the pressure. From this rate it is possible to calculate the value 
of e, the ratio between the number of molecules of oxygen dis- 
appearing per unit time and the number that strike the filament 
in that time. Table XXVIII shows how e varies with the tem- 
perature. 

TABLE XXVIII 
RATE OF CLEAN-UP OF OXYGEN 



Temperature, Deg. K. 

e 
Temperature, Deg. K. 


1070 
0.00033 

2020 
0.049 


1270 
0.0011 

2290 
0.095 


1470 
0.0053 

2520 
0.12 


1570 
0.0094 

2770 
0.15 


1770 
0.0255 



It is evident that e is always less than unity, but tends to 
approach this value with increase in temperature. In order to 
form the oxide W0 3 , at least two molecules of oxygen must 
react with each atom of tungsten on the surface, and from con- 
siderations based on the kinetic theory of gases, Langmuir 
concludes that the manner in which this reaction occurs is as 
follows: The tungsten atoms on the surface adsorb oxygen 
atoms forming a layer which may be represented thus : 





www 

A A A 
/W W W W\ 
That is, oxygen atoms are held on the surface by means of 
primary valencies from the tungsten atoms. Oxygen molecules 
striking this layer combine with the group WO to form W0 3 
which immediately distills off as a single molecule. The layer 
of oxygen combined with tungsten atoms on the surface is 
extremely stable. It will not react with hydrogen even at 1500 
deg. K. This means that the surface of tungsten at this tem- 
perature is completely covered with a layer of oxygen one atom 
deep, and the presence of this oxygen acts as a catalytic poison 
for the reaction between hydrogen and oxygen. In a similar 
manner when a tungsten filament is heated in a mixture of carbon 
monoxide and oxygen, none of the CO reacts with the oxygen 
even with the filament temperature as high as 2800 deg. K., but 
the oxygen attacks the tungsten filament at the same rate as if 
CO were absent. 



Theory of Adsorption at Low Pressures 217 

In view of what has been stated regarding the structure 
of active charcoal and its high capacity for adsorbing gases, 
the experiments on the reaction between oxygen and carbon are 
extremely interesting. "Experiments with carbon filaments in 
oxygen, and in carbon monoxide or dioxide, have shown that 
oxygen acts as a catalytic poison, on the reaction between 
oxygen and carbon, and on that between carbon dioxide and 
carbon. It was also proved that this poisoning effect is due to a 
remarkably stable film of adsorbed oxygen, so stable in fact that 
the filament must be heated in a good vacuum for nearly half an 
hour at 2300 deg. K. in order to distill it off. In this case there 
is very clear evidence that this film consists of oxygen atoms 
chemically combined by primary valencies to the carbon atoms 
forming the body of the filament, according to the formula." 
OOOO oxygen layer. 
II II II II 

c c c c 

c c c c c 
\ / \ / \ / \ / 

C C C C body of filament. 
/ \ 

With carbon dioxide evidence was obtained that the reaction 
occurs as follows : 

C0 2 + C = CO + CO 

(gas) (adsorbed in carbon). 

The reaction between carbon monoxide and oxygen in contact 
with platinum 1 ' is another illustration of the catalytic effect of an 
adsorbed film. The rate of clean-up in this case was observed 
to be directly proportional to the pressure of oxygen, but in- 
versely proportional to the pressure of carbon monoxide. In 
Order to account for this Langmuir assumes that the reaction 
occurs when CO molecules strike oxygen on the surface, but does 
not occur when 2 molecules strike CO on the surface. Thus 
CO acts as a catalytic poison for the reaction at a platinum 
surface. 

It is evident that this theory must exert a profound in- 
fluence on our views of the phenomena of catalysis, a subject of 
immense importance in chemical technology, and there is no 
doubt that an application of Langmuir's theory to this field is 
going to bring about practical results of great value. 

15 I. Langmuir, Trans. Far. Soc. 17, Part 3 (1921). This paper is of special interest as it 
represents the application of the condensation theory to two historically noteworthy cases 
of catalysis by platinum: the reactions, 2 CO +0 2 =2 COt, and 2 H2+O2 =2 H2O. 



218 Theory of Adsorption at Low Pressures 

Evidence for Adsorption Theory from Study of Effect of Gases and 
Thorium on Electron Emission of Tungsten 

The effect of gases in decreasing the electron emission from 
heated metals has been studied in some detail by Langmuir 16-17 
and the observed phenomena are strikingly accounted for by 
the theory of adsorbed films one molecule in thickness. In fact, 
there is a remarkable similarity between the effect of these 
films in poisoning the catalytic activity of a filament and in 
decreasing the electron emission. 

Thus oxygen and water vapor, which react with a tungsten 
filament forming an adsorbed layer of oxygen atoms, both lower 
the emission enormously even at very low pressures (0.001 bar). 
By observing the rate of decrease of emission when gas is let in, 
and the rate of increase of emission when the filaments are 
heated in vacuo it is possible to study the rate of formation and 
also the rate of evaporation of these films at various temperatures. 
"The fact that the rate of evaporation of these films even at 
temperature's of 1800 deg. K. is slow enough to measure proves 
that they are remarkably stable." 

Nitrogen lowers the emission only when voltages high 
enough to cause ionization are used in measuring the electron 
currents. The positive ions formed by bombarding the nitrogen 
molecules with electrons form an adsorbed film on the surface 
of the filament and thus lower the emission. On pumping out 
the nitrogen and heating the filament to a high temperature this 
film gradually distills off and the emission returns to its normal 
value. 

Interesting effects are obtained with tungsten filaments 
containing small amounts of thorium. If such a filament is 
heated in a very high vacuum to 2900 deg. K. for a short time and 
the electron emission at 1800 deg. K. is then measured, it is 
found that the emission is the same as that of pure tungsten. 
By now heating the filament a few minutes at about 2200 to 2300 
deg. K., the electron emission at 1800 deg. K. is found to have 
increased over 10,000 fold, if the vacuum is very good. This 
effect is accounted for on the theory that thorium forms an 
adsorbed layer on the surface of the filament. At 2900 deg. K., 
the thorium, which is much more volatile than tungsten, distills 
off and leaves a surface of pure tungsten. At 2300 deg. K., the 
rate of evaporation of thorium is fairly low, but the rate of 
diffusion through the tungsten is sufficiently high to allow the 

16 "The Effect of Space Charge and Residual Gases on Thermionic Currents in High 
Vacuum,"Phys. Rev. 2, 450 (1913). 

17 "The Electron Emission from Tungsten and the Effect of Residual Gases," Phys. Z. 
15, 516 (1914). 



Theory of Adsorption at Low Pressures 219 

accumulation of thorium atoms on the surface, while at 1800 deg. 
K., the rate of diffusion is so low that no more thorium comes to 
the surface. By studying the rate of increase of the emission at 
temperatures between 1800 and 2300 deg. K., and the rate of 
decrease of emission at temperatures above 2300 deg. K., it is 
possible to obtain data on the rates of diffusion and of evaporation 
of the thorium. 

If a pure tungsten filament is adjacent to the thoriated 
filament and the latter is heated to a temperature at which the 
thorium evaporates fairly quickly, it is found that the pure 
tungsten filament gradually assumes the same electron emitting 
activity as the thoriated filament and there is very strong evi- 
dence that a layer of thorium one atom deep gives just as high an 
emission as a layer several atoms deep. 

The effect of gases in lowering the emission of thorium is 
even more pronounced than in the case of tungsten. An adsorbed 
oxygen layer on the surface of thorium is so stable that it does 
not distill off unless the temperature of the filament is raised to 
2900 deg. K. 

Similar phenomena have been observed in studying the 
effect of gases on the photoelectric activity of metals and there is 
no doubt that in all these cases adsorbed films play an important 
role in decreasing the electron currents. 

Evidence for Adsorption Theory Based on Viscosity Phenomena at Low 
Pressures 

The fundamental postulate of Langmuir's theory that the 
fraction of the molecule impinging on any surface, which suffers 
specular reflection, is extremely small (or more usually, zero) is 
also supported by various observations on viscosity phenomena 
at low pressures. 

In discussing the theory of viscosity manometers* it was 
pointed out that at these pressures there is distinct evidence of a 
slipping of gas molecules over planes. 

At very low pressures the amount of momentum B, trans- 
ferred from a plane moving with velocity u parallel to a stationary 
plane is given by the relation, 

where 8 is known as the "coefficient of slip," L denotes the mean 
free path, rj, the coefficient of viscosity, and a is a constant whose 
value is given by the relation 
8 = aL (62) 

*Chapter III, p. 92. 



220 Theory of Adsorption at Low Pressures 

This relation holds valid only at such low pressures that the 
mean free path exceeds the distance between the moving and 
stationary planes. 

Physically this relation is accounted for, as has been pointed 
out in a previous connection,* by the fact that at very low 
pressures the molecules can travel from one surface to the other 
without mutual collisions. We have here the condition desig- 
nated by Knudsen as that of ' ' molecular flow. ' ' 

Knudsen, 18 Timiriazeff 19 and Baule 20 have attempted to 
derive a relation between 5 and the mean free path (L). 

According to the kinetic theory of gases 

r} = y 3 pQL (10) 

where p = density, U — average (arithmetical) velocity, and the 
factor J/3 has been taken as the average of the values 0.31 used 
by Meyer and 0.35 used by Boltzmann.f 

Substituting for p and ft the relations 

Mp 



\ ttM 



ttM 
we therefore obtain the relation 



8RT 

(5) 



L 3 3 |2*KT (63) 

4 *\ M y ' 



and consequently 



= 3a 77 J2jr 

'" 4 ' -p \ 71 



M 1 ^ 

All the investigators mentioned above are agreed in the 
conclusion that the exact value of a must depend upon the ratio 
between the number of molecules reflected according to the laws 
of specular reflection and the number actually striking the sur- 
face. Knudsen assumes that in general this ratio is practically 
zero. In other words, the momentum of all the molecules striking 
a surface is practically completely transferred to this surface. 
On this basis he derives the relation 

32 d faK . 

a=— .— (bo) 

and determines experimentally the value of C1/C2 to be 0.81. 

*Chapter I, p. 28. 

tChapter I, equations (11) and (12). 

"M. Knudsen, Ann. Phys. 28, 75 (1908); 85, 389 (1911) 
"A. Timiriazeff, Ann. Phys. J + 0, 971 (1913). 
2°B. Baule, Ann. Phys. 44, 145 (1914). 



Theory of Adsorption at Low Pressures 221 

Substituting this result in equation (62), we obtain the 
relation 

6 = 0.917 L (66) 

Timiriazeff, on the other hand, assumes that the amount 

of reflection in viscosity effects is the same as that observed in 

heat conduction at low pressures (see below), and derives the 

relation 

2 — f 2 
S =-/.f L (67) 

where / is the so-called "accommodation coefficient" for heat 
transfer in gases. 

If we assume /=1, as Knudsen does, we obtain the relation 

6 = 0.67 L (68) 

There is evidently here a difference between the deductions 
obtained by Knudsen and Timiriazeff. 

Baule, who has discussed the subject in considerable detail, 
disagrees with the assumption made by Timiriazeff that / has 
the same value for both viscosity and heat conduction. The 
relation derived by him may be written in the simplified form 

x l + s 2 t r^o^ 

5= — -3 L (69) 

where 5 is a complicated function of the dimensions of the 
molecules in the gas and those constituting the surface. The 
value of this constant may vary from to 0.5; consequently 
the value of a lies between 0.67 and 2.0. 

The actual experimental data on this subject are not suffi- 
ciently exact to make it possible to reach any certain conclusions. 
From his experiments on the flow of gases at low pressures 
through capillary tubes, Knudsen concluded that in the case of 
hydrogen there cannot be a specular reflection amounting to 
more than about one per cent. On the other hand, "Millikan 21 
has calculated the coefficient of slip from his measurements on 
the fall of small spheres and has calculated that the slip in air is 
about 10 per cent, and in hydrogen about 8 per cent greater than 
would be expected according to Knudsen 's assumption regarding 
the absence of specular reflection." 

Gaede 22 has made the interesting observation that at pres- 
sures ranging from 0.001 mm. to 20 mm. the amount of gas 

21 Quoted by Langmuir, Phys. Rev. 8, 155 (1916). 
KAnn. Phys. 41, 289 (1913). 



222 Theory of Adsorption at Low Pressures 

which flows through a narrow tube is less than that calculated 
by Knudsen on his theory. This would correspond to a negative 
value of the coefficient of slip, and Gaede therefore concludes 
from his measurements that a certain fraction of the incident 
molecules tend to return after collision in the direction from 
which they came. 

"Temperature Drop" at a Surface in Gases at Low Pressures 

In analogy with the existence of slip in viscosity effects at 
low pressures there has been observed in the case of heat con- 
duction at low pressures between two surfaces the existence of a 
temperature drop at each surface corresponding to a fictitious 
distance 7. This constant is designated as the coefficient of dis- 
continuity of temperature. The analogy between this coefficient 
and that of slip is seen from the relation for the heat transferred 
per unit area per unit time, which assumes the form 

I2—-I1 d+2y 
where k is the heat conductivity. The similarity between this 
equation and equation (42) is evident. 

The existence of this effect, although predicted by Kundt 
and Warburg as a result of their investigations on the coefficient 
of slip, was first observed and investigated theoretically by 
Smoluchowski 23 in 1898. 

Assuming, as Maxwell did in his treatment of slip, that the 
fraction / of the incident molecule is absorbed and evaporated 
again with a velocity distribution corresponding to that in the 
still gas at the temperature of the solid, while the fraction 1 — / 
is reflected, Smoluchowski derived a relation which may be 
written in the form 

Assuming that / in heat transfer has the same value as in 
the case of slip, it follows by comparison with equation (67) that 

7 = fa (72) 

It will be observed that for/=l, equation (71) becomes 
7 = 1.25L 

Actually it was observed that between glass surfaces in air, 
7 = 1.70L and in hydrogen, 7 = 6.96L. According to equation 
(71) this would correspond to the values 0.85 and 0.305 for / in 

"Phil. Mag. 46, 192 (1898); Ann. Phys. 35, 983 (1911). 

*Using the factor 0.31 in Meyer's equation for L in terms of 77, Smoluchowski derives a 
relation with the coefficient 15/4ir in place of 5/4. 



Theory of Adsorption at Low Pressures 223 

air and hydrogen respectively. That is, in the case of hydrogen, 
69.5 per cent of the molecules striking a heated glass surface 
would suffer specular reflection. 

Smoluchowski also suggested another method of considering 
this phenomenon. When molecules with kinetic energy corre- 
sponding to a temperature T\ strike a surface at a higher tem- 
perature r 2 , the molecules leaving this surface have this tem- 
perature only if there is complete equalization of temperature 
during the act of impact on the plate. If this is not the case, 
the molecules leaving the surface have a temperature T inter- 
mediate between T\ and Ti such that 

T-T^aiTz-T!) 
or (73) 

T=aT 2 +(l-a)J\ 
where a is a number less than unity, which has been designated 
as the "accommodation coefficient" by Knudsen. 

At very low pressures, 'where the mean free path is greater 
than the distance between the plates, it can be shown that the 
amount of heat transferred per unit time per unit area and per 
unit difference of temperature between the plates is 

where E denotes the molecular heat conductivity at the tem- 
perature T. 

Since at these pressures 

2y 
it follows that 

k 2 — a ,__, 

y = — 7?>— — ( 75 ) 



p.E' a 



For 


a monatomic gas 






For 


a diatomic gas 


K 


2.5 L 


Hence for monatomic 

7 


-^ = 1.83L 

p.E 

gases 

9—/V 

= ~ a (2.5L 
a 



(70a) : 
(76b) 



and for diatomic gases 



y=— ^(1.83 L) 



*These relations have been calculated from the equations given by Baule for E_and the 
relations derived for k in the kinetic theory of gases. See Chapter I, equations (lob), and 
(10). 



224 Theory of Adsorption at Low Pressures 

For a = 1 we must therefore obtain values of 7 which vary 
from 0.915 L in case of diatomic gases to 1.25 L in that of mon- 
atomic gases. 

Baule 24 who, as previously mentioned, has critically discussed 

the whole problem of slip and temperature drop, has shown that 

it does not at all follow that the accommodation coefficient 

should be the same for both slip and heat conduction. Instead 

fi & 
of the value — = — as deduced by Smoluchowski, he concludes 
7 15 

that - must vary with the nature of the gas and that of the sur- 
7 

face. For the case of a nickel surface he calculates for air, car- 
bon dioxide and hydrogen, the values 8/13, 8/13, and 8/80, 
respectively. These values are in substantial agreement with 
the experimentally observed results. 

Langmuir 24 has adopted Baule's theory as a starting point 
but points out that the latter has failed in his arguments to take 
into account the existence of attractive (and repulsive) forces 
between the atoms on the surface and the colliding molecules. 
The existence of these forces would tend to lessen the velocity 
of molecules after collision and thus modify to a certain extent 
the values derived by Baule from theoretical considerations, 
and the conclusion is arrived at that the probability of any con- 
siderable amount of specular reflection is extremely small except 
in such a case as that of hydrogen. 

Experimentally it has been found that in the latter case the 
coefficient of accommodation for heat transfer is only about 0.19. 
This is lower than that observed in any other case, and Langmuir 
has suggested various reasons for this exceptionally low. value. 
On the whole the experimental work on temperature drop leads 
to the conclusion that the amount of specular reflection in heat 
transfer is ordinarily quite negligible and does not exceed a few 
per cent. 

Recent Experiments of Wood and Knudsen on Condensation 

Some more recent experimental observations made by 
R. W. Wood 25 and M. Knudsen 26 have been interpreted by these 
investigators as indicating that under certain conditions there 
may be considerable reflection of molecules at surfaces upon 
which they impinge. In Wood's experiments a stream of cad- 
mium vapor in a well exhausted bulb was allowed to strike a glass 

24 For a summary of Baule's discussion, the reader may consult Langmuir's paper, Phys. 
Rev. 8, 149 (1916). 

"Phil. Mag. 30, 300 (1915); 32, 364 (1916). 
'•'"Ann. Phys, 50, 472 (1916). 






Theory of Adsorption at Low Pressures 225 

surface at different temperatures. No visible deposit was ob- 
served unless the glass was held at a temperature below about 

— 90 deg. C. On the other hand, once a deposit was started by 
cooling the glass at that spot with liquid air, the deposition of 
cadmium continued even after the deposit was warmed to room 
temperature. 

From these and similar observations Wood concluded that 
while cadmium atoms condense on a cadmium surface at any 
temperature, they condense on glass only if tke temperature is 
below about —90 deg. C. At higher temperatures all the atoms 
are reflected. 

Similar observations have been made by Knudsen and still 
more recently by J. Weyssenhoff . 27 Knudsen experimented with 
mercury vapor and observed that at temperatures above — 130 
deg. C. most of the molecules impinging on a glass surface were 
apparently reflected. With other vapors a similar " critical 
temperature*' was observed above which no condensation 
occurred. In the case of NH 4 Cl, this critical change occurred at 
— 183 deg. C, in that of copper at temperatures varying between 
350 deg. and 575 deg. C, while in the case of zinc, cadmium and 
magnesium, the critical range extended between — 183 deg. and 

— 78 deg. C. All these observations held true only for a glass 
surface. On the other hand, mercury atoms condensed on a 
mercury surface at all temperatures. This latter observation had 
been made by Knudsen in a previous investigation, 28 and in fact 
he had applied equation (7c) to determine the vapor tension of 
mercury at extremely low temperatures from the rate of evapora- 
tion. As has been pointed out in a previous connection, the 
application of this equation involves the assumption that there 
is no reflection of atoms of the vapor striking the surface from 
which evaporation is occurring. 

Weyssenhoff carried out some experiments in order to 
determine the amount of reflection of mercury atoms striking 
surfaces of gold and iron. While no absolute determinations of 
the amount of reflection were obtained, he concludes from his 
experiments that at —100 deg. C, the reflection from gold is 5 
to 10 times less than that from iron. 

These observations have been interpreted by these investi- 
gators as indicating that at some temperature the accommoda- 
tion coefficient for condensation changes very rapidly from zero 
to unity. Langmuir has, however, repeated Wood's experi- 
ments 29 and concludes from his observations that this deduction 
is not justifiable. 

"Ann. Phys. 58, 505 (1919). 

28 Ann. Phys. 48, 1113 (1915). 

29 Proc. Nat. Acad. Sciences 3, 141 (1917). 



226 Theory oj Adsorption at Low Pressures 

In his experiments, Langmuir used cadmium vapor in a well 
exhausted bulb and investigated the effect of cooling a portion 
of the glass surface to different temperatures. He finds that 
"traces of residual gas may prevent the growth of the deposit, 
particularly in those places which have been most effectively 
cooled. This is probably due to the adsorption of the gas by the 
cooled metal deposit." By using a side tube containing charcoal 
immersed in liquid air this effect was eliminated. 

" If all the cadmium is distilled to the lower half of the bulb 
and this is then heated to 220 deg. in an oil bath while the upper 
half is at room temperature, a fog-like deposit is formed on the 
upper part of the bulb in about fifteen seconds. This deposit is 
very different from that obtained by cooling the bulb in liquid 
air. Microscopic examination shows that it consists of myriads 
of small crystals. According to the condensation-evaporation 
theory, the formation of this fog is readily understood. Each 
atom of cadmium, striking the glass at room temperature, re- 
mains on the surface for a certain length of time before evaporat- 
ing off. If the pressure is very low, the chance is small that 
another atom will be deposited, adjacent to the first, before this 
has had time to evaporate. But at higher pressures this fre- 
quently happens. Now if two atoms are placed side by side 
on a surface of glass, a larger amount of work must be done to 
evaporate one of these atoms than if the atoms were not in 
contact. Not only does the attractive force between the cad- 
mium atom and the glass have to be overcome, but also that 
between the two cadmium atoms. Therefore, the rate of evapo- 
ration of atoms from pairs will be much less than that of single 
atoms. Groups of three and four atoms will be still more stable. 
Groups of two, three, four atoms, etc., will thus serve as nuclei 
on which crystals can grow. The tendency to form groups of 
two atoms increases with the square of the pressure, while groups 
of three form at a rate proportional to the cube of the pressure. 
Therefore the tendency for a foggy deposit to be formed increases 
rapidly as the pressure is raised or the temperature of the con- 
densing surface is lowered. 

"On the other hand, according to the reflection theory, 
there seems to be no satisfactory way of explaining why the 
foggy deposit should form under these conditions. 

"Experiments show clearly that when a beam of cadmium 
vapor at very low pressure strikes a given glass surface at room 
temperature, no foggy deposit is formed, although when the 



Theory of Adsorption at Low Pressures 227 

same quantity of cadmium is made to impinge against the sur- 
face in a shorter time (and therefore at higher pressure) a foggy 
deposit results. This fact constitutes strong proof of the con- 
densation-evaporation theory. 

"A deposit of cadmium of extraordinarily small thickness will 
serve as a nucleus for the condensation of more cadmium at room 
temperature. Let all the cadmium be distilled to the lower half 
of the bulb. Now heat the lower half to 60 deg. C. Apply a 
wad of cotton, wet with liquid air, to a portion of the upper half 
for one minute, and then allow the bulb to warm up to room 
temperature. Now heat the lower half of the bulb to 170 deg. C. 
In about thirty seconds a deposit of cadmium appears which 
rapidly grows to a silver-like mirror. This deposit only occurs 
where the bulb was previously cooled by liquid air." 

Langmuir calculates from the vapor pressure data for cad- 
mium that "a deposit which forms in one minute with the vapor 
from cadmium at 60 deg. contains only enough cadmium atoms 
to cover 3/1000 of the surface of the glass. Yet this deposit 
serves as an effective nucleus for the formation of a visible 
deposit." 

At lower temperatures where the vapor pressure is much 
smaller the probability that the atoms striking the glass will fall 
into positions adjacent to atoms already on the surface becomes 
very much smaller and the latter re-evaporate before this occurs, 
consequently there is no apparent condensation. Langmuir 
states the difference between his point of view and that of Wood 
and the others quite clearly : 

''When an atom strikes a surface and rebounds elastically 
from it, we are justified in speaking of this process as a reflection. 
Even if the collision is only partially elastic, we may still use this 
term. The idea that should be expressed in the word ' reflection ' 
is that the atom leaves the surface by a process which is the 
direct result of the collision of the atom against the surface. 

"On the other hand, according to the condensation-evapora- 
tion theory, there is no direct connection between the condensa- 
tion and subsequent evaporation. The chance that a given 
atom on a surface will evaporate in a given time is not dependent 
on the length of time that has elapsed since the condensation of 
that atom. Atoms striking a surface have a certain average 
'life ' on the surface, depending on the temperature of the surface 
and the intensity of the forces holding the atom. According to 
the ' reflection ' theory, the life of an atom on the surface is simply 
the duration of a collision, a time practically independent of 
temperature and of the magnitude of the surface forces. 



228 Theory of Adsorption at Low Pressures 

"The above experiments prove," as stated by Langmuir, 
4 ' that the range of atomic forces is very small and that they act 
only between atoms practically in contact with each other. 
Thus a surface covered by a single layer of cadmium atoms 
behaves, as far as condensation and evaporation are concerned, 
like a surface of massive cadmium." 

In this manner it is possible therefore to account very well 
for the apparent reflection of cadmium and mercury from glass 
surfaces and it is seen that these observations are not all in con- 
tradiction with Langmuir's theory. 

The most recent experiments on this subject are those of 
M. Volmer and I. Estermann. 30 They conclude that for liquid 
mercury, the accommodation coefficient (a) for condensation is 
unity, while for the solid it is slightly smaller. They also state 
that for other substances, such as sulphur, phosphorus and ben- 
zophenone, they have observed values of a varying from 0.2 
to 0.5. On the whole, they are in accord with Langmuir in con- 
cluding that the first stage in the condensation of molecules on a 
crystalline surface consists in adsorption. They, however, make 
the additional assumption that these adsorbed molecules possess 
a certain degree of mobility, thus accounting for the observation 
that crystals produced by condensation from a vapor grow more 
in certain directions. 

Concentration Drop at a Surface • 

As pointed out by Langmuir 31 "the diffusion of one gas 
through another is a phenomenon closely related to heat con- 
duction. In the case of the evaporation of a solid surrounded 
by a gas, where the vapor must diffuse outward through the gas, 
the partial pressure of the vapor at the surface of the solid will 
be less than that of the saturated vapor. In other words there 
will be a 'concentration drop' at the surface, just as there is a 
'temperature drop' in the analogous case of heat conduction, 
and a ' slip ' in gases where viscosity effects are involved. Analogy 
suggests that this concentration drop will be inversely propor- 
tional to the pressure." 

Thus, in the case of a tungsten filament evaporating in 
argon it is to be expected that there will be a difference in the 
concentration of the tungsten vapor at the surface and that 
existing at a distance from this surface, corresponding to the 
mean free path of tungsten atoms in the particular pressure of 
argon. 

»°M. Volmer and I. Estermann, Zeits, f. Phvsik, 7, 1 and 13 (1921). 
"T. Am. Chem. Soc. SI, 419 (1915). 



Theory of Adsorption at Low Pressures 229 

This drop in concentration is a maximum in vacuo and 
decreases as the pressure of argon is increased, thus tending to 
prevent more and more the escape of tungsten atoms from the 
filament. Consequently the actual rate of evaporation of tung- 
sten is decreased by the presence of the gas, as atoms of tungsten 
colliding with gas molecules tend to be thrown back towards the 
surface of the tungsten. 32 

When hydrogen molecules strike a heated filament they are 
partly dissociated into atoms. As a result there is a drop in 
concentration of both atoms and molecules at the surface of 
the filament, and Langmuir has shown how the actual magnitude 
of this drop can be calculated in this particular case. 

Significance of e and its Relation to the Accommodation Coefficient 

Mention has been made quite frequently of the quantity 
€ introduced by Langmuir in his discussion of chemical reactions 
at low pressures. By definition, e is the ratio between the number 
of molecules actually used up in any reaction and the total 
number of collisions in unit time. Thus, in the case of oxygen 
reacting with a heated tungsten filament, e is the ratio between 
the number of molecules of oxygen disappearing per unit time 
per unit area, and the number of molecules of oxygen striking 
unit area per unit time. In the case of reaction between two 
gases, such as tungsten vapor and nitrogen, e is the ratio between 
the number of atoms of tungsten combining with iV 2 molecules 
to form WN 2 and the number of collisions between W atoms 
and A/" 2 molecules in unit time. 

In the latter case, Langmuir finds that e is equal to unity, 
that is, combination occurs at every collision, while in the re- 
action between oxygen and tungsten e is extremely small at low 
temperatures and tends towards unity as the temperature is 
increased to very high values. In order to account for this 
observation, Langmuir assumes 33 that oxygen atoms striking 
the filament condense either as O2 or 0-0, forming either WO2, 
or WO on the surface, and these two forms are in equilibrium at 
any temperature. An oxygen molecule striking WO forms 
WOz which distills off; on the other hand, an oxygen molecule 
striking WO 2 does not react with it. Thus the low value of e at 
lower temperatures is referred to the presence of a very stable 
layer of WO 2 on the surface, and this view is confirmed by the 
behavior of hydrogen-oxygen mixtures in presence of a heated 
tungsten filament. 

3*1. Langmuir, Am. Inst. Elect. Eng., Oct. 10, 1913, p. 1895. 

G. M. J. Mackay, Trans. Ilium. Eng. Soc, Sept., 1914. 
33 J. Am. Chem. Soc. 37, 1139 (1915). 



2S0 Theory of Adsorption at Low Pressures 

In a similar manner, Langmuir accounts for low values of 
e in other reactions between gases and a metal surface by the 
theory that some constituent adsorbed on the surface acts as a 
catalytic poison for the reaction. The point is that the low 
values of e are not due to any reflection of gas molecules from the 
metal surface. There is every evidence, as has been repeatedly 
stated, that the accommodation coefficient is in general 
approximately equal to unity, and therefore low values of e 
whenever they are observed in heterogeneous chemical reactions 
must be accounted for by some condition of the surface. 

It has already been stated that the accommodation coeffi- 
cient for hydrogen in viscosity effects is practically unity. How- 
ever, in the case of heat transfer there is good evidence that the 
accommodation coefficient is much lower. Langmuir has 
observed 34 that at temperatures up to about 1500 deg. K., at a 
tungsten surface, the accommodation coefficient is about 0.19. 
"In other words, only about 19 per cent of all the hydrogen 
molecules striking the filament reach thermal equilibrium with it 
before leaving it." This is in good agreement with the value 
0.26 obtained by Knudsen with platinum at room temperature. 
On the other hand, at high temperatures it is observed that 68 
per cent of all the hydrogen molecules striking the filament 
reach chemical equilibrium before leaving it. "The explanation 
of this apparent paradox is that the surface of the tungsten is 
largely covered by adsorbed hydrogen at lower temperatures, 
whereas at the higher temperatures it is practically bare. The 
19 per cent thus corresponds to the fraction of the molecules 
which condense when they strike a surface already covered with 
hydrogen, while the 68 per cent represents the fraction con- 
densing on a bare surface." 

In the case of the homogeneous gas reactions so far investi- 
gated by Langmuir, e has been observed to be unity. If any 
cases should be found in which it is less than this, the most 
plausible assumption would be that the molecules must collide 
in some particular manner in order that reaction should occur, 
and this might easily be expected where the molecules are large 
and complex. In another connection the author recently 
carried out some calculations on the velocities of decomposition 
and formation of hydrogen iodide. 35 It was found that the 
observed velocities could be quantitatively accounted for by the 
theory that every collision between hydrogen and iodine mole- 
cules is effective in the formation of hydrogen iodide, and simi- 

"J. Am. Chem. Soc. 88, 1147 (1916). 

3&S. Dushman, J. Am. Chem. Soc. 48, 397 (1921). 



Theory of Adsorption at Low Pressures 281 

larly every collision between hydrogen iodide molecules is effective 
in producing hydrogen and iodine. In a similar manner the 
conclusion was drawn that in the case of the dissociation of 
iodine vapor (7 2 ) into atoms, every collision between the atoms 
must lead to the formation of a molecule of I 2 . So that there is 
no evidence that would point to any reflection in collisions 
between atoms or simply constituted molecules. It is, however, 
probable that in the dissociation of such a complex molecule as 
(CH^COOH)j. not every collision between the dissociation prod- 
ucts would result in the formation of a di-acetic acid. Asso- 
ciation would then occur only when certain groups in each mole- 
cule are adjacent. The possible existence of such a "steric" 
factor has been pointed out by other investigators, but further 
investigation is necessary before any definite conclusions regard- 
ing this point can be formed. 



232 



APPENDIX II 



For the convenience of those engaged in high vacuum 
investigations, the following tables have been added, which give 
a summary of formulas from the kinetic theory of gases, molec- 
ular data and various constants. The formulas given in Table 
I have all been discussed in different chapters and are gathered 
together here for convenience of reference. Table II contains 
formulas and data which are of importance in dealing with, elec- 
tron emission phenomena in high vacua. 1 Tables III and IV 
represent an amplification and revision of similar data published 
by the writer in 1915, as an appendix to a series of papers dealing 
with the kinetic theory of gases. 2 The reader is therefore referred 
to this publication for a discussion of the method of deriving 
these constants and for references to previous literature. 

Table III gives molecular data which are of special interest 
in high vacuum work. The values have been calculated from the 
equations given in Table I, for a temperature of 25 deg. C, as 
this is the most usual room temperature. In the calculation of 
the mean free path, the values of rj used were those derived from 
the coefficients of viscosity at deg. C. as tabulated in the pub- 
lication referred to, corrected for 25 deg. C. by means of Suther- 
land's formula. The values given for the molecular diameters 
were taken from the tables given there. For the case of mon- 
atomic vapors from metals an approximate value of the molec- 
ular (or atomic) diameter (d m ) may be obtained from the 
density, p, and the atomic weight, A, by means of the relation 



1 3 pXN 3|pX6.062X10 2 

i~ = \"^r = \ a — 



Hence the number of atoms per cm. 2 required to form a 
layer 1 atom deep is 

l/<i 2 w =10 15 X7.163^-V 

Comparing the values given in Table IV with those pub- 
lished in 1915, it will be observed that the value of Planck's 
constant, h, generally accepted at present is 6.55 X10 -27 . This 
is probably accurate to about 0.15 per cent. The enormous 

II. Langmuir, Phys. Rev. 2, 450 (1913); Trans. Am. Electrochem. Soc. 29, 125 (1916). 
A. W. Hull, Phys. Rev. 18, 31 (1921). 
H. D. Arnold, Phys. Rev. 16, 70 (1920). 

^General Electric Review, IS, 952, 1042, 1159 (1915). See also W. C. McC. Lewis. 
"A System of Physical Chemistry," Vol. Ill, Quantum Theory (1919). An excellent little 
volume on the same subject has recently been published by Armand Colin, Paris. It is 
entitled, "Theorie Cinetique des Gez" par E. Bloch. 



Appendix II 233 

number of investigations carried out in the past few years on 
the determination of this constant have been summarized by 
R. T. Birge 3 and R. Ladenburg. 4 

The former arrives at the value h — 6.5543 =*= 0.0025, while 
Ladenburg concludes that the most probable value is 6.54 X 10~ 27 
erg. sec. The value given in Table IV is the approximate average 
of these. This value had been used in calculating the radiation 
constants in the Planck and Wien equations given in the table. 
It ought to be noted that in recent publications from the Nela 
Research Laboratories the value of c 2 = 1.435 cm. deg. has been 
used. 5 This agrees with the value h = 6.564. On the other hand, 
the value h = 6.55 leads to the derived value c 2 = 1.432. For this 
reason both values of c 2 have been given in the table, and for the 
present it is recommended that in all investigations dealing with 
optical pyrometry the value c 2 = 1.435 be used. 

The value e/m= 1.769 X10 7 is that given by Ladenburg. 
Sommerfeld in his book on "Atombau und Spektrallinien " 
(Nov., 1919) calculates the value 1.7686. In a recent paper 6 
Langmuir has drawn attention to a method of deriving h which 
is independent of Millikan's determination of e (the value given 
in the table). The chemical "integration constant," C, has 
attained considerable importance in recent years, in connection 
with calculations of vapor pressures and equilibrium constants 
of chemical reactions. 7 At present the value usually adopted 
is that based on the equation given in Table IV. 



aPhys. Rev. 14, 361 (1919). 
Mahrbuch d. Elektronik, 17, 93 (1920). 

6 See especially the "1919 Report of Standards Committee on Pyrometry," by W. E. 
Forsythe, J. Opt. Soc. Am. 4. 305 (1920). 



•J. Franklin Inst., May, 1920, p. 603. 



Ladenburg, Jahrb. d. Rad. u. Elektronik, 17, 273 (1921). 



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